nl100 Rush KK vs utg, rivered set

I'm fan of betting sth like 5-8 here, I'm just getting so many curiousity calls from hands like 78 here or sth.

Tim, dont forget timings. Villain snap-pot, hero snap-calls. Turn villain snap-checks and hero snap-check behind.

I'd make it $8 as well.
A big bet will not get called very much because it should be obvious to villain we don't have a bluffingrange in this spot - after we call the flop and check the turn we usually have SD-value.
So either we're going for thin value on the river with a small bet or we hit something and can bet big.
If we wanted to turn a hand like KK into a bluff to get some small Ax to fold, we would start on the turn because we'd need 2 barrels.

So if we bet big here it has to be a strong hand almost always whereas with a small bet we rep a merged range that contains some medium strength hands (on this particular board it's hard for us to have those medium hands, but in general the reasoning above applies).