You shouldn't need 3/8" if you use real paracord - that has a 550lb working weight for a 1/8" rope.

The stuff sold at Home Depot is NOT real paracord, but a weak knockoff. See http://floridahillbilly.com/home-depot-now-selling-paracord-not-really/

So yeah, if you get the Home Depot stuff, you'll need to go with the 3/8" rope - and it will still be only 1/2 as strong as 1/8" real paracord...

Patrik