Lot's of folks are tossing around terms like weight and mass, the amount of weight (or mass) added to the tire+wheel assembly by air.

The air inside the tire is under higher pressure (32 psi) than ambient air (outside the tire, at a nominal 14.7 psi). A greater amount (mass) of air is compressed into that volume, compared to the mass of air the tire volume displaces. So, even though it is "only" air, it is higher density than ambient air at ambient air pressure. All assumptions based on pressures measured at ambient temperature

Given the total amount of air inside the tire (assume a tire volume of roughly 1.25 cubic ft.) at 32 psi, the air inside the tire would weigh roughly 0.163 pounds. Pretty negligible.

Now, re the air vs pure nitrogen...

Air is about 78% nitrogen, about 20% oxygen, and the remainder is argon, carbon dioxide, etc. To make calculations simple, let's just consider air as being composed of 80% nitrogen and 20% air. The atomic weight of nitrogen is 14, oxygen is 16.

Assuming an equal volume of air (this is a "quick and dirty" estimate... no time right now to get in Avogadro's Number and gram molecular weights, mols, etc.), the mass of air would be (0.8 x 14)+(0.2x16)=14.4 and nitrogen would be 1.0 x 14 = 14.

Now the difference between these is probably significant (14.4 vs 14.0) EXCEPT, there ain't a heck of a lot of gas (air or nitrogen) inside the tire to begin with. Using my values of about 0.163 pounds of air, that would amount to 0.158 pounds with an all nitrogen fill.