22 FO: Nut FD on Monochrome

[KneeCo]

22 F0, like 30 shy of the money bubble I think.
Literally my first hand at the table.

Big Blind is t600 (9 handed)

FlopTurnRiver.com (Format: 2+2 Forums)

saw flop|<font color="#C00000">saw showdown</font>

Button (t5200)
SB (t8182)
<font color="#C00000">BB (t14442)</font>
UTG (t15442)
UTG+1 (t17584)
MP1 (t22790)
MP2 (t6588)
<font color="#C00000">Hero (t21756)</font>
CO (t49390)

Preflop: Hero is MP3 with 7[img]/images/graemlins/club.gif[/img], A[img]/images/graemlins/heart.gif[/img].
<font color="#666666">4 folds</font>, <font color="#CC3333">Hero raises to t1600</font>, <font color="#666666">3 folds</font>, BB calls t1000.

Flop: (t3000) 9[img]/images/graemlins/heart.gif[/img], 3[img]/images/graemlins/heart.gif[/img], J[img]/images/graemlins/heart.gif[/img] <font color="#0000FF">(2 players)</font>
<font color="#CC3333">BB bets t1950</font>, Hero calls t1950.

fwiw, I was thinking check behind when I saw the flop.

Turn: (t6900) T[img]/images/graemlins/club.gif[/img] <font color="#0000FF">(2 players)</font>
<font color="#CC3333">BB bets t3625</font>, Hero calls t3625.

I think his bet is kind of weak given the board texture, and I don't think it's a bad call even if my implied payoff on a heart river is very marginally given that I picked up a gutshot and I think an Ace is sometimes enough to (obv I wouldn't count either as full outs given that I'm afraid of AJ/QJ/TJ type hands, but still).

River: (t14150) 8[img]/images/graemlins/spade.gif[/img] <font color="#0000FF">(2 players)</font>
BB checks, <font color="#CC3333">Hero bets t14531 (All-In)</font>

I think this is standard given that he's sitting there thinking I've missed my flush at this point like 100% of the time -- anyone bet less?