Live multi-table game. Started with 35, down to 24. Total chip count is $173,000, avg stack is $7,200. I'm on an 8-handed table with all but two stacks upwards of $10,000 (inc. the chip leader on about $40,000) and, after being down to $1,500, have forced myself up to $5,500. Blinds are $100/$200.
I get dealt

in the big blind.
A player half way round (sitting on a decent stack) raises to $600. Folded round to me and I re-raise to $1,800. He calls.
Flop comes

.
I check. He goes for his chips right away, leans forward, then stops himself and checks after a few seconds.
Turn is

.
Right now, I'm putting him on a couple of high-ish cards but nothing special (maybe KJ or something), and not a pair. After seeing him almost raise me last time I fancy my chances of the check-raise, so check again. He checks immediately.
River is

.
I figure my big initial bet then consecutive checks could be read as AK that missed, so represent the ace with another $1,800. He calls instantly.
Turns over

.
Clearly I screwed up here, but where? I was in a poor position with regard to the table, if not the tournament, so I needed to play big when I got the chance. I'm thinking I should have read more into his check on the flop and made a medium raise on the turn, when there was no danger of a flush and little danger of a straight.
Should I have raised on the turn? Raised on the flop? Raised higher pre-flop? Checked the river?