It's a bit of a hard pill to swallow. The tires have plenty of tread and look good. But, they need to be replaced due to age.
If you're not familiar with it, there is a code on the side of the tire that tells you when they were manufactured.
Also, check your roof. You want to avoid all leaks. A small leak can cause a lot of damage if not repaired quickly.
For roof leaks,
Eternabond and Dicor Self Leveling Caulk are excellent choices for repairs.
Definitely check with a tire shop about changing size.
Please, keep us updated on your progress. Including Pictures. :)