I'm in a NL2 6-max game under the gun and raise 3BB with AQs. Villain in the button calls (he had a VPIP of 42 or so). Flop comes Th8d4h.

I believe that I C-bet to often (I'm still a new player) so I did some research on when to C-bet and when not. This flop was quite wet: both flush and straight draws (though the straightdraw is likely to be a gutshot). Moreover, it had two middle cards, which are more likely to hit my opponents range than my range.

Those are two reasons why I maybe shouldn't have C-bet, but I did it anyways (I'm still a noob ). When later reviewing this hand in equilab, I estimated my equity at only slightly above 50%. He called. Turn comes 7s, which is quite bad for me for the same reason (my equity is now estimated at 40%). I check and he checks back.

The river is Ts, and we both check (should I have bet because he showed weakness by checking back?). He has AJo so I win.

Somehow I feel that I didn't play this hand well. Either I shouldn't have C-bet or I should have played more aggressively once he also showed weakness by checking at the turn. What do you guys think of this?

I would check flop.

AP, turn and river are fine. Better hands are rarely (possibly never) folding if you bet the river.

Check flop is good. Villain will have a lot of hands with decent equity that can call a bet. Top and second pair various kickers, middle pairs, and pockets like 55-77. Straight draws are likely split between a GSSD and a double gutter. The double gutters are often overlooked by newer players. 67s has eight outs not including if it has flush draw or backdoor draw to the diamonds. Decent and bad players will float this flop pretty wide as you don’t have a lot of strong hands and will have a ton of weaker hands. I think it’s a good idea to X but balance it with hands that can X/C and X/R the flop. Your hand has enough equity to X/C. I’d prefer betting hands like QJ, K9, Q9 etc(all suited if they are in your range). They block some of his top pair combos, and there are a lot of turn cards that give you options.
Turn improves villains range 78s, 67s, 77, J9s, and 56s all hit and hands like T9s, 98s picked up more equity.
I don’t like a river bet here with your hand. It has showdown value and never folds out enough pairs or get called by weaker hands enough to justify it. Occasionally you’ll get called by a weaker AX but most of the time you get called by pairs as you represent nothing given your F and T bets.

Against high vpip guys you can range cbet for 1/3. Also notice how this T high flop is better for you then a 9 high flop since you pick up equity on a bunch of turns with your two overs. So we would cbet more frequently on this flop vs lower flops.

You also cbet your suited BDFD hands more frequently than off suit hands (you didn't mention the suit of your AQ) so if you have that then you more incentive to cbet.

Hero in LJ opens AQs; loose, fishy villain in BTN flats. Flop comes Th 8d 4h.

This is a flop that is going to hit a loose, fishy flat-caller's range fairly hard. Depending on the details of their range, they going to continue with something like 45% to 50% of their starting range, or even more if they are sticky with overcards. I would not c-bet here, not without AQ suited in hearts or maybe diamonds.

Turn and river look good.

"Because their check shows weakness" is not in itself good reason to bet. Thinking that way is a leak.

Thanks for the quick replies. I guess I shouldn't have made the C-bet, but luckily it turned out well in the end

you could play this spot in pretty much any reasonable way and make money agasint a 42 vpip

I like range betting against the fish specifically, against a reg don't do that