NL50 Zoom SH - 3 barrel bluff?

Hero (BTN): $56.11
SB: $29.52
BB: $7.64
UTG: $50.00
MP: $52.88
CO: $52.70

Pre Flop: ($0.75) Hero is BTN with A K
1 fold, MP raises to $1.25, 1 fold, Hero raises to $3.75, 2 folds, MP calls $2.50

Flop: ($8.25) 4 J 5 (2 players)
MP checks, Hero bets $4.72, MP calls $4.72

Turn: ($17.69) 8 (2 players)
MP checks, Hero bets $10.13, MP calls $10.13

River: ($37.95) 6 (2 players)
MP checks, Hero ?

Villain plays 22/16 over 66 hands.
Turn: i second barrel because i have decent equity and he doesnt need to fold alot of the times to be profitable, but he's only gonna fold small PP's imo so i don't know if that is enough.
River: Is it profitable to shove? If he can fold Jx it is imo but i never know if i should assume they would.