okay, lemme see if I understand this correctly... You get invited to do stuff with your friends once a week. You THINK it's because you're the last resort. You also THINK they blow you off when you invite them places. Do I have this right?
Okay, if I do then continue reading (if I don't, sorry, just disregard everything after this). Doing things once a week is a lot depending on what's going on in people's lives. School, work, kids, family, etc etc etc.... You can't know what their intentions are, even if you are the last person they ask, that doesn't mean you're their last resort (but I do understand how you could think this). Even if they always pass when you invite them somewhere, that doesn't mean they are blowing you off.
If they make you feel bad, perhaps you should talk to them about it, perhaps you should try to comes to terms with it. Do what you feel you have to do, do what is going to make you better in the long run, but don't jump to conclusions, be 100% sure before you do anything.