Agree that if you bought your tires new and don't run them into the ground you probably shouldn't have a problem. I carry a tire goo kit that weighs a few pounds but includes a bottle of goo as well as a little inflator/pump. As well as the usual- jumper cables, tow strap, crescent wrench, screw driver, reflecto-triangle, (shovel & wool blanket in winter) etc. all in an old Army medic bag. I have no concept of weight, but it is probably lighter than my 15" steel wheel/tire combo.
I would also like to add that a AAA membership card is lighter than all those, but you'd likely have to wait an hour to get help
But yes, no matter what you do, the 12 static pounds are not going to make a difference unless you're really serious about drag racing.