16$ good betting or shove?

[Cawley]

This hand came up from BB wasnt quite sure what he was on with the limp PF but either FD or strong ace, is the betting here fine or are we better with shove on the flop after his raise or the turn?

PokerStars No-Limit Hold'em Tourney, Big Blind is t50 (6 handed) Poker Stars Converter Tool from FlopTurnRiver.com (Format: 2+2 Forums)

SB (t1035)
Hero (t3020)
UTG (t1375)
MP (t2875)
CO (t3815)
Button (t1380)

Preflop: Hero is BB with A[img]/images/graemlins/heart.gif[/img], 8[img]/images/graemlins/spade.gif[/img].
<font color="#666666">2 folds</font>, CO calls t50, Button calls t50, SB completes, Hero checks.

Flop: (t200) A[img]/images/graemlins/spade.gif[/img], 8[img]/images/graemlins/heart.gif[/img], 5[img]/images/graemlins/heart.gif[/img] <font color="#0000FF">(4 players)</font>
SB checks, <font color="#CC3333">Hero bets t150</font>, <font color="#CC3333">CO raises to t550</font>, Button folds, SB folds, <font color="#CC3333">Hero raises to t1400</font>, CO calls t850.

Turn: (t3000) 3[img]/images/graemlins/diamond.gif[/img] <font color="#0000FF">(2 players)</font>
<font color="#CC3333">Hero bets t1000</font>, <font color="#CC3333">CO raises to t2365</font>, Hero calls t570 (All-In).

River: (t6935) 7[img]/images/graemlins/heart.gif[/img] <font color="#0000FF">(2 players, 1 all-in)</font>

Final Pot: t6140