I've heard many people suggest checking the turn for pot control with marginal (overpair/top pair) hands where you're not necessarily willing to play for stacks. But it seems like villain fires big on the river more often than not when the turn is checked through, and I'm never quite sure whether I should call or not.

My "fold to river bet" stat is 68%. Is that too high (Kenny suggested it might be)?

Here are a couple of examples out of many that I could provide -

$0.5/$1 No Limit Holdem
5 players
Converted at

Stacks:
UTG ($78.05)
CO ($110.80)
Hero ($240.55)
SB ($106.35)
BB ($21.75)

Pre-flop: ($1.5, 5 players) Hero is BTN [Jd]
1 fold, CO raises to $3.5, Hero raises to $11, 2 folds, CO calls $7.5

Flop: [3d][Td] ($23.5, 2 players)
CO checks, Hero bets $18, CO calls $18

Turn: ($59.5, 2 players)
CO checks, Hero checks

River: ($59.5, 2 players)
CO bets $30, Hero folds

Final Pot: $59.50

CO wins $87.5 ( won $28.5 )
Hero lost -$29.00


$0.5/$1 No Limit Holdem
6 players
Converted at

Stacks:
Hero ($111.80)
UTG 1 ($97.20)
CO ($47.95)
BTN ($145.35)
SB ($91.05)
BB ($100.00)

Pre-flop: ($1.5, 6 players) Hero is UTG [Js]
Hero raises to $4, UTG 1 calls $4, 3 folds, BB calls $3

Flop: [4s][6s] ($12.5, 3 players)
BB checks, Hero bets $12.5, UTG 1 raises to $25, BB folds, Hero calls $12.5

Turn: ($62.5, 2 players)
Hero checks, UTG 1 checks

River: ($62.5, 2 players)
Hero checks, UTG 1 bets $62.5, Hero folds

Final Pot: $62.50

UTG 1 wins $122 ( won $30.5 )
BB lost -$4.00
Hero lost -$29.00


I'm looking for general suggestions on how to handle these situations (although I realize that "it depends" might very well be the correct answer)

No reads?

Hand 1: the outs you've picked up make this a good 2nd barrel

Hand 2: I don't think you can go far wrong by shoving a strong but vulnerable overpair on that flop

68% folding on the river is comfortably within "normal" range

Shove flop hand 2 imo, has a flush draw or like 77 there 90% of the time.

So nobody folds any of these rivers? Unless villain is supper floaty of bluffly, I think we need to fold both. In hand 1even QJ or flush beat us, so only hand that kinda makes sense is Tx that turned his hand into bluff(not likely)
Hand2: spades got there, 57 got there and we still want to call? Ok he might try to get tricky with 99-TT and VB there but I usually need proof that villain is capable to valuebet thin such hand with 66x+flush on the board.