Is there any advice anyone can give me for assuming the position of weapons squad leader in a light infantry platoon?

Treat your men well, train them better, and lead by example!

If you were selected, you already have the basic skills and leadership attributes to run the squad. You just need to get the experience needed, and you will figure it out. If you are assuming via seniority, you better sit down with your new boss (PSG), get briefed and pray there isn't a live fire scheduled anytime soon.

Go to Ranger school, start dressing for the job you want. Before you know it, you will be the PSG.