I weigh 230 and I did a sprint tri in May. My goal was to run the entire run portion, and I did (although the bike leg was my best leg, woo hoo!). I've also run several stand alone 5Ks and a 15K. I am slow -- so very slow, 15 minute miles slow. But I followed the Couch 2 5K plan, and worked my way up to running slow and you know what? I love it. I am not good at it, but I love it. I always thought I had knee problems and so couldn't exercise, but I manage just fine and don't actually have any joint pain. Biggest suggestion is invest in GOOD running shoes -- go somewhere to get a run assessment, etc. (or, if you decide to do the minimalist running thing, start even slower).

I really think the couch 2 5K plan was key for this working for me -- it's just the right balance of challenging but not overdoing (do NOT cut out the walking warm up and cool down!). I was amazed that I want from total non athlete to triathlete in 8 mos. (Started C25K in Sept of last year, started spin classes in Nov and bought a bike soon thereafter, and then started swimming in January, culminating in the race in May).

Be careful, of course, check with your doctor, the usual. But really? Go for it! I found I felt better, wanted to eat better, and I did lose about 20 pounds (i've regained 10 after falling off the wagon a bit, but am starting to creep down again).