Quoted:
There is no standard "medium profile".

There is no 16" A2.

We'll need to know specifically what barrels you are looking at.  Molon had a weight comparison post a while back which compared the weights of a bunch of different 16" barrels.  I'll look for it.

ETA:
http://www.ar15.com/forums/t_3_118/515797_16_Barrels___Countours_and_Weights_.html
Not many midlengths in there or variety of manufacturers though.

Quoted:
Here
and
Here

If you read the barrel description,
One is described as medium profile, and the other as A2 style profile.
Both are 16"

I was trying to figure out which upper would weigh the most.

Quoted:

They are likely identical.  The one described as a "medium profile" is not what I would call a medium profile, it looks like an M4/"government" style (AKA "A2") profile in the photo.  One is hammer forged, the other probably button rifled, which is probably the only difference.  That would be a question for the vendor.

Dissipator style uppers in my experience are very nose heavy because of the heavy front sight base so far out on the barrel along with an additional gas block, exacerbated by the profile which puts a thicker diameter/more weight at the muzzle end of the barrel.

A vastly lighter weight solution would be to use a lighter weight profile barrel with a low profile gas block and a rifle (or longer) length free float handguard with iron sight on the handguard rail.  If you're using optics this makes it easy to just use fold down sights for both front and rear.  If it's primarily an iron sight rifle, my own opinion, as someone who has tried dissipator type configurations, is to just get a regular midlength gas barrel and maybe use a finer match-type sight post, depending on the rifle application.  Just too much weight out at the muzzle which makes for poor handling.