Cash game at DTD - blinds £0.50/£1
It is very late and we are currently 5 handed.
I am on the button with

I have around £135.
I am wanting to play any two half decent cards because I am in a favourable spot. The BB is very well chipped up (over £400) and now a little drunk and raising every single hand, the French guy to my immediate right is playing his cards face up (he tells me he is new to the game) and the Chinese guy, the SB to my left, is the complete opposite to the stereotype with no gamble in him whatsoever.
I limp because I am 90% certain the BB will raise anyway whereas he doesn’t always call a raise. Anyway, true to form he raises on the BB to a paltry £3. Frenchie calls, so do I and SB passes.
Flop is

Happy days, I have flopped a straight.
BB leads out for £11. Frenchie calls.
Mmmm.
For some reason I sense some strength from the BB and if Frenchie has called he probably has a flush draw or some such. Still, I am a believer in putting money in the pot in order to win a decent amout so I re-raise to £30. At this stage if only BB calls this won’t be a terrible result.
They both call. There is exactly £100 in the pot.
Turn is

Ouch, a diamond.
BB checks, Frenchie checks and for some bizarre reason I check behind. Ok, not that bizarre - I am in position and looking for more info on the river here, and also keeping the pot down (I know; I just said I like to bump the pot when I am ahead, but of course now I may not be). Frenchie could well have a flush and beginners just love to check the nuts.
The river is a blank, for arguments sake the

BB checks ( but I still have this gut feeling that he is relatively strong) and so does Frenchie.
Ok, so I must bet the river, but how much please? The relevant factor here is that Frenchie has £75 behind and I have about £100.
As I see it I have BB beat and will probably get a call. At no stage has he re-popped me so he doesn't have AJ.
I might not have Frenchie beat, although given that he is very WYSIWYG, I reckon I'm 70% likely to be beating him, given his two checks.
Six scenarios are possible -
a)They both fold, unlikely.
b)BB folds, Frenchie calls and wins, I lose a big pot
c)BB calls, Frenchie calls, and Frenchie wins the lot
d)BB calls, Frenchie calls and I win the lot
e)BB calls, Frenchie passes and I kick myself for not betting more
Or
f)BB calls, Frenchie shoves it in, I call and BB calls also, this scenario is effectively the same as c) only I lose more money
So given the above, how much do I bet on the river? I think I bet the wrong amount and would like some thoughts please. Thanks.