Background:
Hero has been playing for about 2.5 hours. Villian has been at the table for about 1 hour.

Villain seems competent, bought in for $600 (matched the biggest stack).

Definitely not a drooler. No reads otherwise.

We had just chopped a hand preflop when it folded to us in the SB/BB. We turned out hands over and I had QQ in the BB.

This means I picked up QQ the very next hand in the SB.

Positions:
BU V ($700): Youngish Hispanic F
SB Hero ($250): Young AM, tight

Preflop:
Folds to V on BU
BU opens to $13
Hero 3! to $40 with QQ
BB folds
BU says: "Pocket pair again?"
BU calls

Flop ($83): JJ5
Hero checks
BU checks

Turn ($83): JJ53
Hero bets $30
BU calls

River ($143): JJ534
Hero bets $45
BU raises to $145

Hero action?

Notes:
1. Is the flop a mandatory c-bet on this kind of board? I didn't c-bet this board because I was thinking I should keep my range wide by checking (i.e. what if I had AK, AQ, TT, 99, 88).
2. The flip side to this thought is that she would peel at least 1 street with an underpair or two overs.
3. when checked to, shouldn't BU almost always bet small Jx here for value (i.e. even if I had AQ/AK, I should call a reasonably sized bet at least one street, otherwise I'd be too exploitable)?

I go just a smidge more preflop ($45) to do a better job of preventing setmining odds plus helps negate the disadvantage of playing OOP to a non-drooler (where we're going to be put in gross spots on A/K high flops).

SPR is 2.5 so we're completely committed at this point; if outflopped us, he gets our stack, nice hand sir. If we had AA (or maybe even KK) I wouldn't mind a tricky flop check as much since our hand is so much less vulnerable. But with QQ there's just that much more overcards that could come, which sucks when we feel committed. I mostly just PSB here to make it look like I'm getting out-of-hand (we didn't just get a big pocket pair back-to-back, did we?) to get the rest in on the turn.

I'm also betting the turn as played but much more. I don't like the fact that we committed ourselves preflop and setup a lol SPR of 2.5, and yet by the river we've somehow left ourselves with >> PSB left.

Admittedly river action is gross. Some will say our small sizing / weakish looking postflop play has induced a bluff. But there are no draws for this guy to be chasing and our slowplay could be exactly what it is (a monster looking to induce). I don't think we end up inducing here nearly as much as we think we do, and dude likely just has it.

But I would have been trivially all-in on the turn, so whatever.

ETA: Regarding Button betting a Jx when checked to on the flop, there is no reason for her to bet with this small of SPR and in position and on this drawless of a board. She knows she can play for stacks whenever she wants plus she's fine giving you a chance at hitting whiffed overs. A stoopid bet of lol $10 or whatever is fine but a check behind is completely reasonable as well, imo.

GcluelessNLnoobG

I'd bet the flop. As gg says, no need to give free card to random Ax/Kx hands. And you can expect to get at least one street of value from pocket pairs seeing this fairly innocuous board.

I'd go half-pot tho, to give villain a chance to try a raise and also to give cover to when you wanna cbet your AK/AQ in this situation. (I'm protecting whiffed AK/AQ by betting everything rather than checking everything)