bet.
you have a strong hand with 2 pair, especially if it's top 2 and even better if block a flush draw out. for example, you have kd8h on a kh 8s 2h flop.
by betting, you get value for your big
hands and you force your opponent(s) to pay for their draws. are they going to hit? yes, sometimes. but that's just how the game goes, you still want to charge them because you're winning more often than they're hitting. especially if you block one of their outs, it gives them less chance to hit and you're winning more.
also, by betting, you set yourself to take your opponents chips, which is what you want to do because more chips = more value. you make more money when you have more of your opponents chips and you set yourself up to do well in mtts when you have more chips, especially if you are able to knock someone out of the mtt. by checking, you miss out on a street of betting, which is missing out on a street of value. also, by checking, it's much harder to stack off an opponent because the pot is smaller. and that's not what you want to do if stacks are short enough for you get get max value.
lets say the pot in the example hand example above is 8 bbs and effective stacks is 25 bbs. if you check the flop, villain only has to call 1 street of betting to see if they get their flush. lets say you bet 7 bbs on a blank turn and villain calls. pot is now 22 bb, with 18 bbs effective. river is a brick. you bet and villain folds. you essentially lost out on 18 bbs.
but lets say you bet the flop for 7 bbs, pot is now 22 bbs with 18 bbs effective. turn is a blank and you jam for 18 bbs. villain now has to call 18 bbs to win a pot of 40 bbs, given them improper
odds to call on a flush draw and you now have a much better chance to stack your opponent because if they want to see the river, they have to call off the bet. they might still fold, but you still have the opportunity to stack them if they call, which you don't have if you check.
now, this isn't to say checking is a good. it depends on the situation. if you're against an opponent that likes to semi-
bluff their draws a lot or is just really aggressive, you might opt to check and call down their bets.
but if you're checking because you'd rather see the turn to make sure you're not 'losing' a lot of money if the draw hits, well, you're still losing money when the draw doesn't hit becuase you're missing out on a street of value. with big hands, you want to go for 2-3 streets of value.