I am trying to lose weight but will having nuts such as peanuts and edamame stop me from losing weight?

No. 

Too many calories (or sometimes too little calories) will hinder weight loss. 

Nuts will affect your weight loss negatively if you eat too many of them. If you can limit yourself to small portions, they make a good snack.

However, I wouldn't rely on them for protein too much. Maybe it's because my diet is high in protein, but I would have to eat loads of them to meet my quota for the day. Eat them, though. They're very satisfying, full of healthy fats (which you seem to desperately need in your diet) and they might curb your sweet tooth if you have a problem with that - at least they do for me.