Yes, your opponent's may know your weakness but you know theirs too, right?
So that should give you the same, level playing field immediately.
At a certain, even intermediate level of tennis, we know most of our opponent's weaknesses but that doesn't mean that we are able to exploit them.
It's one thing to know what to play and completely different to be actually able to hit the necessary shots to take advantage of that weakness!
I suggest two things:
1. Work on your backhand so that you don't feel it's a weakness anymore. Be realistic though. You don't have to make it a weapon, but just a solid stroke that won't break down after a few shots.
And it's not really the stroke that breaks down most of the times, it's your mind. Stay strong and every time someone plays to your backhand and they DON'T win a point (or get a short ball), this PROVES to you that the backhand is not weak.
2. Accept that you will ALWAYS have some weaknesses. No one is perfect. The game of tennis though is not about weaknesses and strengths, but about who can better:
- make the most of own strengths
- protect own weaknesses
- neutralize opponent's strengths
- take advantage of opponent's weaknesses
If you play points, then the only thing that matters is who wins and not what kind of weaknesses you have.