The point behind weight training is to improve strength and general health.
There has been an endless argument about strength training for cyclists. I'm not going to argue that going to the gym will help your speed or anything like that. What I would say is that gym work can be very healthy for other reasons. First, it's a mental break. The gym helps you focus on your muscles, helps you learn how to use them. Simply put, a mental break is something that takes your focus off your target, and the gym is a good way to do that. Second, the gym strengthens your supporting tissues. Have you ever heard of those plaguing knee problems that cyclist often get, well, if you strength train (and stretch) you're less likely to get these type injuries, including back and shoulder problems. In building these supporting tissues, strength training also allows you to build a platform for cycling specific muscles (fast and slow twitch), meaning over the long haul you'll be able to build more speed. Third, strength training builds confidence. Building strength in the gym will help you feel stronger than your competition, and if that's the edge that puts you across the line in 1st vs. 2nd, then it's worht the effort.
Anways... you don't need to go to the gym to get strength training in. But if you only have 1.5 h a week, I would focus on your cycling muscles. Lunges, squats, leg curls, leg lifts, etc. In that 1.5 h you should be able to do 3 sets of 15 reps at a very low weight. Remember, the idea is not to build bulk, so avoid putting on those big plates. I use the bar without any weight for the first half of my gym period. Core muscles can benifit a lot from routine strengthening. Strong abs are always a favorite with the wife/girlfriend. Core muscles are important when ballancing the force against the pedals. Your legs are pushing down, and it's your core that keeping your body from getting all mangled up. Strengthening the core also helps prevent injury to the lower and upper body. If you do do an upper body workout, work those bis/tris/and deltoids... cyclists tend to have weak rear delts, making our shoulders curl forward when sitting in a chair.
You can get a lot of strength traingiing done at home. Push ups, sit ups, chin ups, pull ups, lunges, etc.. all are great, and don't require equipment.
Last but not least, a recent study out shows that strength training in cylists is important to maintain and build bone density. You've be surprised how many cyclists end up with low bone densities in their later years. I assure you, breaking a hip when you're 85 years old is not fun. Best to start working on preventing that now.
And if that doesn't get you motivated... think of all the cute girls who need to be looked at.