Party Poker 2/4 Hold'em (9 max, 9 handed) FTR converter on zerodivide.cx

Preflop: Hero is UTG+1 with [As], [Qh].
1 fold.

Flop: (5 SB) [3c], [Td], [2c] (2 players)
SB checks, Hero bets, SB calls.

Turn: (3.50 BB) [Kc] (2 players)
SB checks, Hero bets, SB calls.

River: (5.50 BB) [Ac] (2 players)
SB checks, Hero checks.

Final Pot: 5.50 BB

Im HU against a loose player. Anyone recommending checking the turn? If so, elaborate.

Hit my card on the river...but now there is four to a flush, check is ok?