Beans do not root from the stem, so there is no benefit to burying them deep... and it can actually contribute to damping off. When transplanting, you should just barely cover the original soil line.

Beans grow leggy if the light is insufficient. If planted in the same place, they will likely continue to get leggy, until they either fall over, or die.

Thanks!
I've moved them into a window that doesn't have someone else balcony over it and they've started growing broader leaves and aren't leaning as much now so hopefully they'll be okay at this point. Re-potting them into window boxes tomorrow so we'll see how it goes.

I start a lot of my beans in peat pots in a grow light but move them into a greenhouse as soon as they emerge from the soil. Otherwise they grow tall and weak.