It seems like the consensus in today's games is to use a variety of flop bet sizing options based on specific flop textures. Some people are using multiple bet sizings on one type of texture but for the simplicity of the question let's just assume we're using 1 bet size for each "texture class."

A few general observations:

All hands are HUNL. Let's assume BTN is 95% and BB is 80%-17% 3bet.

BTN 2.5x, BB call
Flop Qc4d4s
BB check, BTN .33p

BTN 2.5x BB call
Flop Ah8d3s
BB check, BTN .4p

BTN 2.5x, BB call
Flop 9h8h5s
BB check, BTN .8p

There's quite a significant difference in the player pool's average bet sizing choices on dry flops like Q44r and wetter flops like 985 2tone. It doesn't seem like either flop texture would be one that we're doing a lot of protection betting on (which we might be doing on a flop like 832r). I've been trying to come up with some possible reasons for the sizing changes on these board textures. I have a few points but none of them are really sticking out.

1) Choosing a bet size based on how elastic or inelastic BB's continuing region is.
2) Sizing larger when BB's average continuing hand has significant equity against BTN's value region (on 985hh for example).
3) Choosing a size that targets infliction points or range asymmetries. For instance on Q44r ranges will be fairly symmetrical but BTN will also have all of his AQ, OP combos that BB's range will be lacking. OOP's range also has a massive subset of unpaired hands lower than a Q. This big gap makes it tough for OOP to get near 1-A continues when we choose to bet 1/3 pot.
4) Sizing flop based on how likely our hand will be able to bet 3 streets. For instance our value region on Q44r or A83r will often still be a value bet on the majority of run-offs. However on 985hh a significant portion of our flop value region won't be a value bet on a lot of run-offs, so they're more incentivized to put in 2 fairly large bets rather than 3 medium sized bets.
5) Pinpointing the optimal sizing for our average value bet on the flop and then filling that region in with bluffs. (The issue I have with this idea is on A83r wouldn't our average value bet (something like AQ) prefer to start sizing quite large to max vs the worse Ax subset that calls down 3 streets? We won't have many 3x/8x that bet and we'll have plenty of air to fill in a larger sizing.

I'm hoping we can get some better arguments here or someone can eliminate a few of the points I made.