Hero: I've been at the table for ~30 minutes, I've raised 2 times pre, and I haven't shown down a hand yet. I won both pots, one pre flop and one post flop. I've played with these people before today, and I have a LAG image. Depending on the villain some view this as competent LAG and some think I'm just a spew box.

Villain 1: Older guy, calls IP when late in the action very loose, I've played with him before. Thinks I raise too much pre and calls me down light.

Villain 2: ~35 guy, calls very tight pre, raises tight pre IP and OOP. Knows that I'm perfectly capable of bluffing big, but won't fight back without a minimum of TPTK, and sometimes not even that.

Preflop:
Folds to hero and I raise to $12 with JJ
V1 calls from the BTN
V2 calls from the BB

Flop ($33): K98
V2 checks
Hero?

What's my best play?

I'm not keen on putting more money in this pot at the moment. We just don't do that well against there ranges. Check.

Not in love with the texture of this board, but I cbet this most of the time. Your hand is good a lot of the time here, and giving a free look at the turn doesn't seem like a good idea to me, villains should have mostly drawing hands in their range. The K hits your range harder than theirs.

Cbet 25 for value/fold to aggression.

I like betting as it doesn't sound like they will raise draws.

The problem with checking back this flop is we can never win the hand unless our opponents are absurdly passive.

Totally disagree with this (or well, at least to the extent I would say loads and loads of villains are absurdly passive) If you really think this do you check AK because button is 100% to bet with a range we crush?

I'd say it is this exact unjustified fear that drives lots of players into spewy cbetting (not that it is horrible here)