rivered set vs shorty - call, fold or shove?

villain was 20/5/1 AF over 44 hands with 100% cbet.
He vbets most of his range on the flop so I can call imo. The turn is checked and I hit my set on the river. I vbet and he minraises me.

I figured slowplayed QQ, AQ, a str8 with AK and 2pair hands like QJ etc.

Folding seems gross. Calling seems ok and shoving means I win vs 2 pair but lose to QQ and AK. Whats my best option?

Poker Stars No-Limit Hold'em, $0.10 BB (8 handed) - Poker Stars Converter Tool from FlopTurnRiver.com
Hero (BB) ($10)
UTG ($5.05)
UTG+1 ($21.42)
MP1 ($8.45)
MP2 ($3.85)
CO ($10.72)
villain (Button) ($5.26)
SB ($12.13)
Preflop: Hero is BB with 10, 10
5 folds, villain bets $0.30, 1 fold, Hero calls $0.20
Flop: ($0.65) 3, Q, 6 (2 players)
Hero checks, villain bets $0.30, Hero calls $0.30
Turn: ($1.25) J (2 players)
Hero checks, villain checks
River: ($1.25) 10 (2 players)
Hero bets $0.89, villain raises $1.90, Hero ?

Terrible turn to check with QQ or JJ. You're looking at AK or 2pair. Combos aren't favorable. Just call.

doesnt really matter what you do as long as it isnt raise

flop is close, don't raise river