This proposal is also on Balancer's forum.. The proposed code to implement it can be found here.
Proposal to have 45k BAL (~31% of the weekly distribution) allocated as an extra incentive for liquidity between BAL and uncapped tokens (WETH, DAI, USDC, WBTC). Wallets flagged as Balancer Labs shareholders don't qualify for this "liquidity staking" extra incentive. The main goals are to significantly increase liquidity on key BAL pairs and to allow non-shareholders to compound their BAL holdings at a much faster pace, accelerating protocol decentralization.

The importance of BAL liquidity can't be overstated:
TRUER PRICE DISCOVERY: it improves trading conditions for all market participants (lower spreads and less slippage for both buyers and sellers), allowing for a more transparent and effective price discovery process;
SUPERIOR LP INCENTIVES: a stronger token (with higher price inertia) results in a higher quality for the incentives given to LPs (liquidity providers) via liquidity mining;
SHARPER GOVERNANCE: it opens doors to a new class of invaluable stakeholders and protocol governors (e.g. larger investors, especially those heavily involved in and experienced with DeFi protocols);
BROADER GOVERNANCE: with no participation from Balancer Labs' shareholders (more on that later), liquidity staking will accelerate BAL distribution and protocol decentralization by giving all other BAL holders the opportunity to compound their governance rights at a much faster pace;
SAFER GOVERNANCE: pools are non-custodial and BAL in them retain full voting power (i.e. no need to withdraw liquidity to vote), such that high liquidity and a healthy governance are not in conflict;
Balancer itself being a DEX, it feels only natural as the ideal venue for high BAL liquidity to be incentivized. Finally, it's worth noting that allowing a high portion of the token supply to be concentrated on centralized exchanges could expose the governance to significant risks, as illustrated by the episode with STEEM.
The 145k BAL weekly distribution to LPs on Balancer is calculated proportionally to the adjusted liquidity contributed by each LP. This adjustment is made by applying (i.e. multiplying) a few factors to their liquidity measured in dollar terms.
Naturally, the value of those factors can be:
1, having no effect;1, acting as a penalty (when the liquidity is deemed less useful);1, acting as an extra incentive.A feeFactor ≤ 1 (see proposal) applies a small penalty to pools with higher fees.
For each pair inside a pool, we apply:
a wrapFactor of:
a BRF (BAL & Ratio Factor), which is the combination of a ratioFactor ≤ 1 (see proposal) and a stakingBoost ≥ 1 (described in this proposal and with further calculation details specified in its ammendment).
BRF = stakingBoost * ratioFactor
{BAL & uncapped_token} (uncapped tokens currently being: WETH, DAI, USDC, WBTC, BAL), then its stakingBoost = 1 (i.e. the incentive doesn't apply to this pair).The current BRF will only depend on the characteristics of the pool (its tokens and weights), and may have a maximum value of 1.54. It looks like this:

After looping through all possible pairs in a pool, we combine their factors (via weighted average) and the result is a wrapFactor and a BRF for the whole pool.
Finally, we calculate and apply a tokenCapFactor adjusting down the liquidity of a token when it exceeds a predetermined maximum. Except for the 5 uncapped tokens already mentioned, all tokens eligible for liquidity mining are currently capped at $10M each. See more details on how to calculate it and the recent changes to how token caps will evolve.
This is a proposal to have 45k BAL (~31% of the weekly distribution) allocated as an extra incentive for liquidity staking.
This extra incentive is:
all BAL distributed as a result of applying a
stakingBoost > 1to the liquidity of{BAL & uncapped_token}pairs, from wallets which are not flagged as shareholders of Balancer Labs.
The remaining 100k BAL would be distributed to all LPs in all eligible pools, disconsidering the effect of a stakingBoost (i.e. all liquidity being subject to BRF = ratioFactor).
The constant value now would be: STAKERS_SHARE = 45000 / 145000, and we can then calculate the unique value for stakingBoost that satisfies this target distribution.
The intended result is for BAL liquidity on Balancer to increase substantially, but in a self-regulated way.
The simple yet powerful idea is: as BAL liquidity gets higher the extra incentive to staking gets diluted among stakers, so that our constant target for STAKERS_SHARE is met.
In a more visual approach:
when non-shareholder BAL liquidity is low, the stakingBoost will be high, resulting in a high BRF (a hypothetical scenario being the orange curve in the graph below, in which BRF peaks at 12), so there will be a very strong incentive for BAL liquidity to increase;
when non-shareholer BAL liquidity is high (the desired scenario), the stakingBoost will have come down to lower levels, resulting in a lower BRF (a hypothetical scenario being the green curve below, in which BRF peaks at 3).

We first calculate the liquidityPreStaking: the total adjusted liquidity from applying all factors, but with stakingBoost = 1 (i.e. BRF = ratioFactor). Let's say the result was $200M.
We will need to apply a yet unknown stakingBoost so that:
STAKERS_SHARE = (finalLiquidity - liquidityPreStaking) / finalLiquidity
... which can also be stated as:
finalLiquidity = liquidityPreStaking / (1 - STAKERS_SHARE)
In our example:
finalLiquidity = $200M / (1 - 45000/145000) = $290M
We may apply any temporary tempStakingBoost > 1 to {BAL & uncapped_token} pairs from non-shareholder LPs, resulting in a tempLiquidity. Let's say our result was $230M. This would mean the tempStakingBoost increased the adjusted liquidity in $30M, while what we actually want is an increase of $90M.
Now to get the desired stakingBoost, we only need to "stretch" or "shrink" the tempStakingBoost according to the ratio between the two liquidity adjustments (desired & temporary):
(finalLiquidity - liquidityPreStaking) / (tempLiquidity - liquidityPreStaking) = stakingBoost / tempStakingBoost
... which in our example would result in:
(290 - 200) / (230 - 200) = stakingBoost / tempStakingBoost
stakingBoost = 3 * tempStakingBoost
An important aspect of this proposal is that Balancer Labs shareholders (investors, advisors and founders) seem aligned with the spirit of the proposal: to accelerate governance rights distribution. In order to achieve this goal, their wallets will be excluded from participating in liquidity staking. This restriction doesn't apply to eventual BAL they hold that are unrelated to their shareholder allocations, for instance BAL bought on the market or earned through being LPs with tokens other than their BAL shareholder allocation.
Here is the complete list of shareholder addresses to be excluded from liquidity staking.
Note: wallets currently tagged as "Balancer: Shareholder XX" on Etherscan are actually vesting smart contracts which hold mostly locked (i.e. yet unvested) BAL. Vesting happens continuously and linearly over a period of 3 years which started at token launch (2020-06-20). When finally vested (i.e. free to transfer), BAL can only be withdrawn to the respective beneficiary address of each vesting contract. The addresses listed above are the 51 unique beneficiaries of the 51 vesting contracts. All the BAL balance they already hold is vested.
The community is willing to tolerate up to about 10k BAL per week per shareholder being sent to centralized exchanges as they are cognizant of shareholders also seeking to deleverage their BAL positions over time, without attempting to subvert the exclusion list. In case some large BAL balances move to third-party custody solutions held in segregated addresses or to multisig wallets (both situations are likely to happen), the current list may be updated to reflect those new shareholder addresses as also excluded from liquidity staking.
The community will have the prerogative to update this list so that changes are effective already before any still pending weekly distribution.