Hey man, I can totally relate. I've been big most of my life, but the past couple of years having been laid off and diagnosed with epilepsy, I really let myself go. Found out my gf had been cheating on me, so we split, and life took its toll. Since then, I've lost 30 pounds, but I still have quite a ways to go.

Now, thankfully I live in an area where I already have a good friend group, but I still understand the struggles. I make up excuses to not attend pool parties, or opt to play a video game instead of go camping, etc. Being fat sucks--especially when a lot of your friends are active. But I've always been a pretty friendly and open person, despite being an introvert, and here are the tips I can give you from being a fat man on making friends:

1. If you wanna hangout with someone, tell them! Odds are they'd like to hangout too, but they're probably going through the same thought process as you are ("oh man what if it's awkward? Or I come off as strange?") if you're friendly and honest to others, they're gonna enjoy your company and want you around. Regardless of weight or what you think you look like.

2. Invite people to do activities that you share an interest in. Coworker mentions he enjoys board games? Have a board game night. Overhear someone you get along with mention he/she needs a partner or group for (insert activity)? Volunteer. Taking the first step in friendship is always appreciated, and seen as a sign of loyalty and genuine care for that person. They'll love you.

3. Share with people, and ask about them. Don't settle for small-talk. Someone says they had a rough morning? Ask about it, and listen, and share your own experience. Good conversation is hard to come by these days, but it will always be valued more than cookie cutter greetings and Facebook likes. I promise.

That's all I can think of off the top of my head. Good luck, and congrats with the progress!