You played it a little passively. If you're gonna raise (especially in 6max) give em a little meat. Not 3BB more like 6BB. After that, calling the 3 bucks is ok. Drawing with 2 overs is not a bad draw (25%). Turn you shoulda re-raised and ended it there. River: What did you think he had? You felt like sticking with it and got lucky. Next time, don't let a 6 scare you. Into a raised pot when the board paired 6s you shouldn't even need to worry about them.
-'rilla