Type of resume paper?

I hope someone can give me some answers here.

I have been complemented many times on my resume and cover letter so no problems there. I worked very hard to tweak it just right and I get complements that it is very professional and not full of fluff and lies.

My question is: does it matter the type of paper I use? This may sound stupid, but I was told in a class to use high grade, high weight paper and envelopes for professionalism. Then I just read that using these make me sound pretentious. I personally like the weight of the paper as it's not as flimsy as regular old printer paper. Also, I'm hoping it stands out with other resumes. The weight I'm using now is 32lb, color light grey. Envelopes match. Envelopes also are printed by my printer and not hand written.

I know this is a nursing forum (I am an aide) but am studying political science and am sending out resumes and cover letters to local law firms because I want to work as a paralegal after graduation before going to law school. I am taking some paralegal classes so I will have some experience there.

In your experience and in your opinion, is this pretentious? I want to come off as professional.