There's a whole sub-section of the running community that advocates following planned run/walk intervals. I did that for years, even ran half and full marathons that way. A great resource is
http://www.jeffgalloway.com/
The most important thing is to find a pace that you can sustain over some period of time. Maybe that's walk briskly for 5 minutes and jog for one minute, then repeat. Or walk 2 min / jog 2 min. Whatever is sustainable and reasonably comfortable. It doesn't feel like a "failure" if you go out with a specific training plan.

You should feel like you are working, but not puffing so hard that you can't carry on a conversation or you get a side stitch. Over time, as you build endurance and continue lose a little weight, you will find that you can increase your jogging intervals and maybe eventually eliminate walking altogether. Or maybe not -- Galloway claims that the walking intervals extend the time that you are able to continue, and also helps prevent injuries because they give your legs and joints a break.
If weight loss is your primary goal right now, then it is better to walk briskly for 30 minutes (with an occasional minute or two of jogging) than to kill yourself trying to run and dying after 10 minutes. When I started my most recent weight loss journey at 150 pounds, I couldn't run at all anymore, I just died in 5 minutes. (and 3 years previously I had completed a full marathon!!) I simply did the "brisk walking" thing for several months until I lost part of the weight, then started the run/walk intervals. As I built my endurance up again, I found that I didn't need to walk as much. Then one day it all clicked, and I found I didn't need the walk intervals at all. But that took months to get there.
So, don't give up, but maybe slow down a bit! It takes time to build running endurance, but you can definitely get there with persistance.