Haven't been there myself in June or July, but I do know that it is HOT.
Other than that, weather should be good and water temps warm.

I don't know where you are hearing these things.  Ramon's is *way*
over-rated.  There's plenty of better bangs for your buck.  What are you
after?

And as far as the rainy season?  That's in late fall, just after hurricane
season.

Vis can be good and it can be crappy.  Currents are not a problem.  Winds
can be a problem.  Marine life is good.

I love San Pedro.  Go, you'll love it too.  I've spent 100+ days there, 6
trips over a four year period.

I have been to Abergris Caye at all times of the year - mostly, in fact, in
the summer (including August).  It's not hot at all - since you are right on
the water with a constant sea breeze.  Of course, I am from Houston, so in
the summer, getting away from 100 degree heat to 89 degree heat is welcome.
The rains come and go - mostly in the late afternoon and very early morning.
Not a problem at all.  Just convection thundershowers.  Visibility does
depend on the winds.  If you get strong currents, visibility can be
fantastic (100+ feet).  If the air is quiet with little wind (rare, but can
happen), the water stagnates from the tidal flushing of the lagoon -
essentially the lagoons waste hangs around the reef because there is nothing
to move it out.  Diving in those conditions is eery and makes you feel like
you are diving up north for lobster.  These conditions hang around for a
couple of days at a time and then just as quickly - gone.  Crystal clear
again.

So go - and have a great time.  No shoes are needed...even in the
restaurants.  The Panty Ripper is the best drink on the island.