NL25z OOP 3b pot, OTR value jam or explo fold?

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NL25z OOP 3b pot, OTR value jam or explo fold?

Blinds: $0.10/$0.25 (6 Players) BN: $52.52
SB: $27.68
BB: $104.03 (Hero)
UTG: $25.00
MP: $32.99
CO: $34.66
Opponent is a reg, no other information
Preflop ($0.35) Hero is BB with K Q
UTG folds, MP raises to $0.63, 3 folds, Hero raises to $3.01, MP calls $2.38
BBvMP, KQs is included as a 3b for me and I sized up, as were a bit deeper than 100bb
Flop ($6.12) 7 T 7
Hero bets $2.02, MP calls $2.02
Probably a board we can allow ourselves to cbet entire range, since im also 3betting 78s/76s in this spot or TT PF, we should have the advantage
Turn ($10.16) 7 T 7 K
Hero bets $6.33, MP calls $6.33
Getting value from draws and few weaker Kx, some strong Tx
River ($22.82) 7 T 7 K 3
Hero checks, MP bets $21.63 and is all in, Hero folds
In game, I didnt feel to good about pulling this value bet through, since there isnt too much worse wed get called by. I would expect hes capable to arrive here also with slowplayed 7x. On the other hand, check folding here feels pretty stupid. I looked at the solver solution and it had 16 EV for betting and 6 for X/C.. but with the X/C, it also lets the opponent bluff with every sort of missed hand (AsQx, AQs, FDs, 98s, QJs..), and I see some of those but not all.. am I just overthinking and it should be a jam, or maybe something in between (like betting 30% to get calls from Tx as well, folding to raise mostly)?
Final Pot MP wins $22.82

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