This hand came up in a local WPT event (not the main event for the series) that had a $340 buyin. Everyone started the tournament with $15K in chips and the structure was good with 40 minute blinds. At this point of the tournament the blinds are 100/200 and there is a 25 ante. Hero started the hand with around 13K in chips and was in the small blind on this hand.
It's folded around to the cut-off who calls the big blind. Button also calls. Hero looks down at A:hearts: Q:clubs: and also calls. (Hero did not want to raise here and give the cut-off and button the opportunity to re-raise). Big blind checks. Pot now has 1025.
Flop is A:diamonds: 8:clubs: 7:spades:. Hero checks the big blind bets 500. Cut-off and button both call. Pot now has 2525. Hero raised to 2500. Big blind and cut-off call, button folds. The pot now has 9025.
Turn is the 7:clubs:. Should the hero now check or bet? If betting how much and why?