5NL FR JJ vs UTG raise

Opp is 13/5 at the time of the hand. Only 20 hands so not very significant.

I have him on 88+,AQ pre. I always hesitate to reraise or not with JJ, but as I have been aggressive the last orbit, and am barely ahead of his range I decided to just call and play it for overpair/set value.

His check on the flop does not necessarily mean much because he could be doing it with his whole range. Missed with overs, careful with a medium PP or even slowplaying AA or KK or a set and planning to check raise. I figured that with his check he is more likely to hold AK or AQ than the rest, and that the flop missed most of his range, and I bet the pot to get value from these hands.

Comes his call, the turn and his 40% pot bet. Really puzzled at this stage and wondering whether this is a blocking bet / semi-bluff with a draw or a slowplayed set / high pair or even maybe just a dumb bluff with an AK he can't let go. I really don't like any of my options here.

Same story on the river, can I ever not call the 1/3rd pot bet? I know he is not often showing down AK or 99/TT, but some opps also do that as a small bluff with missed draws.

Flame away, because I really need to learn to play these stupid spots and get better post flop.

No-Limit Hold'em, $0.05 BB (8 handed) - Hold'em Manager Converter Tool from FlopTurnRiver.com

saw flop

BB ($1.95)
UTG ($4.93)
UTG+1 ($5.01)
Hero (MP1) ($5.87)
MP2 ($2)
CO ($5)
Button ($5.42)
SB ($5.07)

Preflop: Hero is MP1 with J, J
BB bets $0.20, 2 folds, Hero calls $0.20, 4 folds

Flop: ($0.45) 2, 8, 6 (2 players)
BB checks, Hero bets $0.45, BB calls $0.45

Turn: ($1.35) 7 (2 players)
BB bets $0.55, Hero calls $0.55

River: ($2.45) 7 (2 players)
BB bets $0.75 (All-In), Hero calls $0.75

Total pot: $3.95

Edit: converter has a problem, opp is UTG, not BB