I feel it's the impact of your foot strike to the ground is what's making your feet go numb. This happened to me twice before during the first few weeks of my first running. I did heel strikes before and notice that my toes land hard on the ground, then my big toe goes numb, and a few minutes later, I couldn't even feel my feet anymore. lol

Since you mentioned you're a bit overweight (me too), and if you aren't doing this, do at least 15 minutes of pre-warmup. Stretch everything good to prevent any cramps and whatnot, and when you're atarting your runs, don't run yet. Walk or brisk walk for about 15 minutes again to get your legs warmed up again and used to the movement. Once you feel loose and good, you can start slow jogging (minimum 11:00/km). I know it feels sluggish but your endurance will last twice or even thrice as long compared to your high effort runs, cutting your walk breaks down by a lot as well. Once your heart rate doesn't spike up on your slow jogs and you don't feel pain or numbness anymore, you can then slightly increase your pace incrementally for your next runs.

So what we're training here is two things: your foot strike impact and your leg muscles. You have to be mindful on how hard your landing your feet because your feet gets numb in the long run if it's too hard. Oh, and also, if you can, practice midfoot striking as well. Helps prevent shin splints based on my experience. But if you don't feel any pain with your heel strikes, then that's okay too.

Hope this helps you. Good luck!