played correctly?

Folded around to my SB(0.25/0.50)...I have 45h - raise to $2. BB calls. BB and I both have $50 in our stacks. I have seen BB play and is a solid player and is capable of making quite a few different moves.

Flop 5d7cQd - I bet $3 and he raises to $6, I call.
Turn 4s - I check (thinking check-raise) and he checks
River 8h - I bet $4 - he raises to $8

check/call or check/fold depending on the size of his bet on the river

I don't like making raises with suited connectors preflop when I won't have position after the flop. I used to do it all the time, but realized it was a significant leak in my game and have since stopped. On the button I make that play all day tho.

As played, I think you played this fine. He raises you on the flop which means he likely has Q. He checks behind you on the turn which suggests to me that he has a weak Q (like QJ, QT). On the river since you didn't check raise the turn, he is confident (rightfully so) that his weak Q is good and raises your 'steal' bet.

You called and won the hand, right?

I called and he showed 66 for the straight. He played this rather well....I will have to make sure I don't sit with him on my left anymore.

had me fooled.

not hard to do.