Okay so I've faced this situation a few times, and not sure what line do you guys prefer. Here's the hand...

1/2, 6 players, new table, assume everyone is bad/average/passive/limp-happy


UTG, CO and BTN limp, Hero completes K7 in SB, BB checks << basically everyone has ATC

Flop ($10): K K 7
Hero bets $5, only BB calls (we're both $200 deep)

Turn ($20): Q
Hero ?

Preflop: is slightly debatable and I'd lean towards a fold often, but the table is apparently terrible, so I complete.

Flop: I opt to lead out for a small size because of the FD, expecting them, 7x and other random hands to call, and an unlikely case King to raise.

Turn: is where I'm not sure if I should be going for the check/raise to get max value from the flushes or just continue betting hoping flushes will raise, and some other hands, perhaps those with a spade, will continue calling. I'm pretty sure betting out again is the superior option, and perhaps I'm only being results-oriented, here's why:

Turn ($20): Q
Hero bets $12.50, V calls

River ($45): 9
Hero bets $22.50

everything seems fine I'm not checking the turn I wanna get money in there. c/r will represent a flush+ and fold out worse. Pre is prob the bottom of a complete range on a weak table.

This is the sort of situation where you need to exploit villains tendency to think in terms of absolute dollars not pot size. A pot sized bet seems small and your stacks are deep, so go for more the whole way.

On the flop KX are not going away and flush draws are likely to over pay. I would bet $10, possibly even $15 if I think I can get flush draws to call. Turn is better a bet then a check/raise. The check/raise might even scare off a small flush, if not on turn then on river. Better to go ahead and bet $15-$20. Same on river, go for $30.

Bigger on the flop.
We can easily bet $10 here and get looked up by all sorts of flush draws and anyone who has a K.
We might lose a little bit of value from middle pocket pairs and strong 7's that might have called a bet here on the flop, but the value that we get from a flush draw on the flop greatly outweights the value from 7x and 88-JJ here since the flush draw will be calling more on later streets and the 7x won't be.

On the turn, the bet sizing is a little bit better, but could still be bigger. I would have bet $15 as played. If we made the flop bigger ($10 - $12) I would go a similar % so $22 - $25.

The river is a pretty terrible card for a lot of his range. If he has Kx he is likely going to fold to most decent sized bet, and a lot of flushes are now a 1 card flush that can't feel that great about their hand.
I like the sizing as a %, but if we had a larger pot at this point, I would have bet larger on the river with the larger sizing.

PSB/PSB/PSB. Get money in with monster hands asap in small limped pots. I'd only slow down if a nit raised me.

In a limped pot you won't be able to get stacks in without some cooperation from villain(s).

Rather than bet 1/2 on flop I'd just go pot. It is still a small $ amount but will help grow the pot if anyone has enough to come along. I might even overbet the pot - either they have a K or a FD they want to continue or they don't. The pot is tiny now so I'm going for max value when they have it and throwing away the $15 I might get out of a weak hand if I play it real slow.

Against an unknown at a seemingly passive table I just keep betting pot on turn. I think it actually helps them raise you because it looks like you have KX if you potted or overbet flop and then it looks like you're overvaluing it on turn. If they just call at least you still built the pot.

River I bet close to pot again hoping he has As or KX he can't let go or 77.

So: Flop I bet $15. Turn is $40 and I bet $35. River is $110 and I bet $75. Don't mind missing all the little wins if I get a big pot once in a while.

Also if you overbet this flop and showdown a flopped boat it will enable you to pick up limped pots more frequently with pot/overbet semibluffs the times you don't flop a boat

You definitely should be betting more. I'm probably over betting pot on the flop and potting the turn so we're in a good position for a river shove. With 100bb effective and unknown Vs, I'm not slowing down. If I don't make it to showdown then I have good information to use later.

This, exactly.