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It is hard in situations like this when you know you have the upper hand, yet the guy with the big stack is going to be pushing you around and most likely calling all of your bets no matter what you did, and potentially out drawing you because of it. The only thing I could think that you may have done differently, if you thought there was a possibility he would fold, is just to take down the pot right there by betting bigger. When there is an overpair on the flop, you get into a dangerous situation because anyone holding that overcard to make trips could outdraw you even though you have a boat on the flop.
In my opinion it wasn't the smartest move on your friends part, even with trip aces on the flop he is dominated by anyone with that other ace and kicker better than 6 (and of course pocket 3's). If he knew you were holding pocket 3's, which obviously he didn't, I doubt he would have made that bet with only 4 outs to beat you. But then again I don't know anything about how the game prior to this hand unfolded, or anything about either of your playing styles. I think it's pretty clear you made the right call, especially seeing as you were short(er) stacked and could use some leverage.
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