That is a big drawback to growing veggies in small spaces, and I don't have much of a solution -- other than to maximize the edges of the balcony. Grow things in hanging pots, train them up a trellis along the edge -- try to make the most of that vertical plane of light.

At one point I had acrylic, outdoor mirrors along the side of a balcony, which redirected some light. I don't think it was really strong enough to compete with actual sunlight, but it did seem that plants didn't bend quite so hard to the sun-side.

Maybe you could plant less light dependant veggies, like chard and lettuces on the inner side of the balcony?

Good luck!

I have the same problem. I'm in shade, and also have a patio above me that has a rug on it, so no light from there. I'm going to try lettuces and maybe pole beans.