Weight limits on bikes are to protect the company from liability and are usually pretty conservative. It's not that the bike will fail if someone significantly heavier rides it, it's just that you can't go after the company for warranty or liability if it does. There are some companies that make bike specifically for heavier riders like
http://www.worksmancycles.com/ or you can look at a touring bike which is similar to a road bike but with a more relaxed geometry and which is made for carrying heavier loads.
IMHO, instead of buying a trainer or spin bike, put the money into a bike a grade up from the one you are considering and/or invest in a tougher rear wheel if you are worried about weight. Even in Phoenix you will be able to ride year-round. During the hottest parts of the year, just ride in the early morning or late evening rather than mid-day. On those days where you absolutely can't ride outside, do some kind of cross training like swimming, yoga/pilates, or weight lifting (aka resistance training).
I have kind of the opposite situation up here in MN, where the roads get bad or the wind-chill becomes life threatening in the winter and there are often a few weeks at a time that I can't / won't ride due to the risk. It's not that I physically can't ride on ice and snow, it's that the roads become narrow and rough and the other traffic can't swerve, slow or stop as well. I use a spin bike at the gym some, but also focus on cross training for core and upper body strength during that time. It's not a bad idea to have other physical activities so that you can take a break from cycling once in a while. Even the pros take time off the bike from time to time.