Check & fold. I don't know why people think check-raising is a good idea here. Let's look at your opponent's possible starting hands:
AA-you're beat & he might have a better draw
KK-you're beat & he might have a better draw
JJ-you're beat
TT-you're beat
AK-if he has a heart, you're slightly the better of a coin flip as he has 2 overcards w/ a better draw
AQ-if he has the A of hearts you aren't that big of a favorite

Easy fold. Get out of this hand before you lose any more money!