Called a C-Bet with Overcards

[Cougar]

Villain is 37/9/7 over 35 hands, Flop C-Bet: 50% (1/2)

Decided to call flop with the 2 overcards, was this a bad spot to mix up play?

Any good rules of thumb when thinking about calling down a c-bet with 2 overs (e.g. Flop C-Bet>80%, other reads)?

Got a nice turn card, now what??

Didn't feel that my hand was strong enough to overshove, too good to fold, tried to get to river cheap but that was only semi-effective.

What are other better ways to play and think about this?

PokerStars No-Limit Hold'em, $0.02 BB (9 handed) - Poker-Stars Converter Tool from FlopTurnRiver.com

BB ($2)
UTG ($0.71)
UTG+1 ($2.98)
MP1 ($5.12)
MP2 ($3.77)
MP3 ($0.95)
CO ($1.81)
Hero (Button) ($1.98)
SB ($7.08)

Preflop: Hero is Button with A, Q
UTG calls $0.02, UTG+1 bets $0.10, 4 folds, Hero calls $0.10, 3 folds

Flop: ($0.25) 3, 10, 7 (2 players)
UTG+1 bets $0.16, Hero calls $0.16

Turn: ($0.57) Q (2 players)
UTG+1 bets $0.52, Hero calls $0.52

River: ($1.61) 2 (2 players)
UTG+1 bets $0.70, Hero calls $0.70

[Gshark]

Not sure if I'm calling here. Really depends on what the villain's range is to raise 5x pf. You're not thinking he has an overpair?

His line reads like KK to me. Especially with the turn and river bet. Am I wrong?

As played, I'm thinking I'd shove on the river or fold. If I think I'm ahead then the shove is the right move, and if I think I'm behind then I don't see the point in calling - seems spewy to me.

[surviva316]

i'm probably avoiding this situation altogether and folding preflop. even when you're in position playing against a preflop raiser with this hand is ALWAYS going to be hairy.
then i don't get calling the cbet at all. what are you putting him on making this play? most likely hands are a pocket pair (which even if you hit your queen or even your ace you're not certain you sucked out on him) or he has AK and you're screwed even if your ace hits. if you think he missed with the flop then you should raise but i think this is a bad play too because his stats don't show him to be very aggressive so it's so likely he has something.
i'll hand it to you that it's hard to evaluate the turn and river, but i simply would never put myself in that situation

[2ndline.4thstreet]

It may be a nitty play, but I'm folding pf. As played - I really hate being a station in this hand. Raise it on the flop or turn at least. River too. If you're going to be in this hand I say play it!

[KeeKoLy]

Depending on what the player has been raising with, I don't think the call PF is that bad. If you knoew he's raising in EP with not so great hands this is not a bad play to call. Assuming you did call, I would think you have to raise the turn here.

[AFchung]

i wouldn't toss this preflop, but i'd probably fold the flop. i don't see much reason to get into sticky situations we can easily avoid