wp...nothing you can do about it....definetly betting turn without a heart in my hand....like sizings as well

Fold the river. You have enough flushes of your own to prevent villain from leading here. HOWEVER: if your villain read this:

Name: Clarkmeister
Theorem

Reliability: 8/10

Overview: If the river
card brings the 4th card of the same suit, you should bet out if you are first
to act and heads up against an opponent. The Clarkmeister poker theorem helps
you to pick out a prime bluffing opportunity, although it is useful to have an
understanding on your opponent's style of play for this theorem.

**** *** ***

Betting or checking the turn does dictate how villain might act on brick rivers.

If you check on the turn flush card, villain may be more inclined to bluff his missed straight draws and some light flop peels. 

Hi, 

Standard. Versus an unknown opponent (probably a occasional player) I would hit that turn 100% times.

Regards,

Could somebody please (briefly) explain to me why betting the turn is the right play? I'm trying to figure it out but I can't. Thanks.

Big Blind [now] has a wider defending range, so his flop continuing range will have a lot of non-Ace high broadway hands that are gut shot draws or middle pair + BDFD. The bet is to protect versus those. 

Remember, betting with different hands on different board textures are more lucrative than others. Your bet here is doing better than checking but not by much.