I’m very glad to hear that there are bigger buys out there that run really good times. It gives me hope. I fluctuate between 239lbs and 242lbs and right now my 3 mile is officially 21:40 for a total of a 278 PFT. I’d love to have that 19:30 and I working hard to see that I get it. I’m doing intervals and long distance and slowly but surly my time and weight is falling. Any advice would be appreciated!
Do a mixture of high and low intensity runs, you're trying to increase your VO2 max. The shorter, high intensity increases the amount of O2 your blood can carry to your muscles (plus trains your fast twitch fibers). The longer, slower runs will let your body recover as well as teach yourself the feeling of running that distance.
One thing about being heavier and running, or at least for me. I can't stress enough about having a good, not worn out, pair of running shoes. It'll save you so much stress on your knees. Also, and again this is also for me, but if I don't work out/run at least 5 times a week, I'll lose speed really quick. Right now, probably couldn't hit a 19:30 due to flying so much, but I know I could if I got back into it properly.
Good luck. Nothing more satisfying as a fat ass like myself blowing past someone on a 5k or the PRT