Should I get a padded strap for my 7.5lb guitar?

Right now i have a squier strat which is 7.5lbs and a 2.5" nylon strap that came with it. after 30 minutes of playing my shoulder starts hurting. i'm looking at getting a levy's soft suede strap (http://www.guitarcenter.com/Levy-s-Soft-Suede-Guitar-Strap-360547-i1129750.gc) which is also 2.5", but i'm wondering if that would still hurt my shoulder with my heavier guitar. If so i would get the padded version but I don't want to spend the extra $30 if I don't have to.