You can reasonably change tires up to about the 16" size. I'd use a bottle jack rated substantially higher than half the max axle weight, e.g. an 7000#-8000# jack for a 10,000# axle. You will probably need some wood blocks too, since most bottle jacks do not have a long shaft and cannot lift very far. And you need a BIG lug wrench, since the bolts are torqued tightly, well over 100 lb-ft.
A large 16" tire and wheel are going to be around 100 lbs. Getting it off the spare mount (and getting the old one back on) is going to be arduous and dirty.