As one who has already gone down this road and has 6 yrs. experience I can tell you that you may not want only a light weight chair, but an ultra-lite chair. "Light" chairs can be 15 to 20lbs., an ultra lite can be as low as 12 to 15. Check out the website for Spinlife.com. I've found that they have the best prices on the web and free shipping on anything over $50. They are reliable and quick. They will work with you and your insurance company.
I don't see why you have to see a PT to be evaluated, my neuro signed my papers for me and when I had to order a replacement chair my regular pcp did it.