I feel like I run into this situation a lot in both live and online, particularly in multiway. The general line goes ...
1. Postflop checks around to me (last to act) and I Cbet and 2+ people call.
2. The turn provides me with no further equity so I decide to take a free card when it checks to me.
3. The river does not complete draws so OOP villain fires a sizeable bet and I fold a junk or marginal hand.

Example hand:
Preflop 100bb effective
UTG+1, HJ limp in.
Hero at BTN raises to 3bb with JhTh
SB calls, BB folds, limpers both call

Flop comes Td, 2h, Qc (15bb pot)
Checks to me and I decide to fire a CBet 1/2 pot due to disconnected board texture and my backdoor draws (BDFD, three to straight). Everyone calls.

Turn comes 2c (45bb pot)
Checks around to me. Because I gain no equity, I decide to check back for the free card.

River comes Qd (45bb pot)
SB fires out for 25bb. Everyone else folds. Hero?

In general I feel like this line of flop aggression followed by turn checkback for a free card gets easily exploited on river by more aggressive players. I think a lot of players read turn checkbacks after flop action as weakness and try to steal river pots OOP and often winning mainly because they had the first opportunity to show aggression. I'm put in a spot where I need to make a thin call. Whenever the info is available to me, I feel like I'm often wrong. I called down too light, or I folded to a bluff, or I raised into a monster.

Has anyone struggled with these situation? What helped?

Thoughts:
1. I could checkback the flop to hide hand strength and consider turn delayed cbet or even raise
2. I could "check strong" on the turn more with borderline hands like second pair? I feel like I try to do this but the situations come up so rarely
3. I could double barrel with a wider range on the turn, but this seems dangerous esp in these multiway pots.