Sorry for the late contribution to this post, but I have very strong opinions about this and just wanted to share.
Having had access to a historian, with experience with archived documents, I asked this same question. He suggested that any historical document you want to last should be printed on archival grade paper. This should be a durable, acid-free paper. This is what legal, historical or documents with significant value are printed on. He further suggested that a cotton rag paper be used.
The certificates should be printed on paper that will last. The office paper most certificates are printed on will yellow, become brittle and then deteriorate and decay in a matter of years, considering most people do not store their certificates in a climate controlled location, out of the humidity and temperature fluctuations. Also, just because a paper looks like it is parchment or is a heavier stock, does not automatically mean it is archival quality and will last.
We settled on 100% cotton, 32-lb paper. In the past this was purchased from paper supplier Xpedx, however they have since changed their business model and do not have any retail stores.
Most recently, I have used Southworth, 100% Cotton, 32 lb, white business paper. These come in packages with anywhere from 25-250 sheets per package. And a fairly reasonable price, for the product you are getting (Amazon, 250 sheets, $24).
I really like the look of a parchment type paper, but I had to put my preferences aside and think about the certificate recipient and the desire for future generations to have access to the document. This made switching to the acid-free, cotton paper a no-brainer in my mind.
Thanks for letting me chime in.