I don't see why the weight would be an issue - one of my best friends was well over the healthy weight range, yet she was one of the most popular girls I knew, due to her bubbly personality. The speech impairment may be the bigger issue - if people are having trouble understanding you, then it's going to be difficult to hold a meaningful conversation with them, which decreases your chances of developing meaningful friendships. Have you ever worked with a speech therapist? It might not be a bad idea to do so, both for the sake of your future friendships AND future career (where communication skills may be vital to your profession).
I am a lot like you, in that I'm content with being alone and doing my own thing the majority of the time. Like you said, though, it can become lonely after a while. My advice is to do what I did: force yourself to go to social events, even if you don't feel like it. I highly recommend you live with other college students, whether it's in a dorm or apartment - that way, you will be forced to interact with other people, and you'll be "in the loop" about what's going on around campus. It takes practice, and it seems you are sorely out of practice. Just as you have made a choice to spend your free time at home, you now have to make a choice to put yourself out there and meet new people. Otherwise, old habits will most likely lead you down the same path you went down over the last two years.
Join clubs. Talk to the people around you in lectures/classes. Ask your roommates if they want to grab a bite to eat at the cafeteria. If you can, work part-time and chat with your
co-workers. Get involved in study groups. Whenever an opportunity arises, go for it. It will take time, but you'll start to see some improvements as the months pass. Just keep at it! Show interest in your new acquaintances, and try to get to know them on a more personal level. Most won't be interested in return, but some will, and those are the friendships you want to spend the most time developing.