Re: How many calories would you burn in a one hour class?
When I first began Aikido, I also struggled with being out-of-shape. The problem I found with Aikido is that it just isn't aerobic and/or anaerobic enough for the time period given (30-40 minutes of actual workout time). My solution: work out just prior to coming to Aikido. It got me highly motivated for Aikido, I already came in with a good sweat going and already warmed up and ready to go. You don't have to do anything hardcore, maybe an hour of powerwalking...low impact and excellent cardiovascular workout. It worked for me. No gym fees...only the cost for a good pair of walking shoes and an extra gi or two..since you'll be washing them more often...since you're sweating profusely from the moment you walk into the dojo!
Also, if your interest in Aikido is more self-defense oriented, then this is truly the most effective way to study Aikido...when your tired & exhausted. Why? It more closely simulates the reality of self-defense application. Rarely will you be completely ready, either physically or mentally. Learning how to use it when you're not at 100% will make your self-defense skills more directly applicable to a real-world scenario. This is the tried and true method that the military uses.
For what it's worth...