I think a reraise pre would be in order, btn min raise probably looking to snag the blinds although he should have went bigger to do that.
It then becomes tricky post-flop as that is certainly a draw heavy board, IMO however the overbet screams underpair or flushdraw (granted this is from my experience in lower limits than 10nl so I could be completely wrong, however looks like a please fold bet or the nuts as QT is certainly in sb range to call minraise pre).
The check call on the turn looks to be a flush draw, either this or they have the QT or 7T of hearts in which case they have a redraw to the abs nuts if the river spikes a heart although in either of those cases I don't see why they would have pulled a check/raise line.
The river I deff check back fiven how many possible combinations they could hold which now has a T and your only getting called if your beat.
Just my thoughts, granted many others on the forum that may have some different thoughts which I also look forward to. I think a raise pre would have simplified the entire hand some as would enable to be more specific on the sb's possible range.