also, just weekends is a good start ... it's better than no days isn't it? If you really get on and want to do more you can always increase. If you think to yourself "i'll go every other day" you are setting yourself up to fail
Everyone in the gym are there for exactly the same reason as you so don't worry, no one will be in the least bit concerned what you're up to. Go for it.
I used to go to the gym, swimming and various exercise classes a lot, I never gave a monkeys about anyone else who was in there, I was too busy focusing on what I wanted to do.