I played in the £50 (2) rebuy tourney in notts last nite. Am deep-stacked with around 40,000 chips (average is 16,000) and blinds are 600/1200 with 40 left. Folded round to Mateyboy on my right (who actually has 43,000) and is on the button. He raises it to 2,500, I call on the SB with

and BB also calls. I know the way mateyboy plays and he is usually quite a tight/aggresive player. Anyway, flop comes

. Now, BB (who has 16,000) raises 3,000 and mateyboy calls. I thought his call was weak because if he had trips, two pair, even a straight he might wanna protect against that board. I put him on AK/AQ and I pushed all-in. BB folded and mateyboy thought for an eternity before calling with

and won the pot. I thought it was a very good/ very lucky call and I while I know I would have folded in his position, surely I'm the only one to blame.
Should I have?
a) flat called the raise after the flop?
b) folded pre-flop/post-flop?
c) could i have taken him off the pot raising say, 15,000 after the flop and then all-in with the blank on the turn? Maybe the over-bet signified a drawing hand?