The serious runners that I know use Brooks, Mizuno, and Asics.
The problem is that those are runners, and we're not all runners. Most of us just run/jog to cross-train.
I'm someone who as an athlete wasn't overweight even when I got up to 260 pounds (I was around 10-11% bodyfat at that weight). Nikes, Mizuno, and Asics were torture. It wasn't until I bought New Balance that my feet wouldn't hurt after just a few miles. They designed a specific pair that was like a bespoke shoe designed specifically for me, but came off a manufacturing line-- the 586NV. It was designed for larger and heavier athletes with maximal cushioning and motion control (not weight) as the chief design ambitions; specifically to counter pronation. It was also the only large shoe company at the time that manufactured shoes in multiple widths, so I was able to get the "EE" wide. I liked them so much that I ended up buying two more pairs in case the line got canceled. Fantastic decision.
Because they're so heavy competitive runners tend to hate them, but I didn't care, and I figured, if anything, that was just more strength. I did time myself on runs, and made an effort to progress, but it wasn't like I was worried about reaching certain times during my practice runs such that it mattered how heavy my shoes were. Racing wasn't my sport, so there was no need to train "sport-specific" with really lightweight running shoes because I wasn't trying to complete my practices runs as preparation for a race. All that mattered was conditioning and progress, not my time itself. I wasn't trying to be Prefontaine.
Looks like the modern version of this shoe is called the 1540v2:
http://www.newbalance.com/pd/new-balance-1540v2/M1540-V2.html?dwvar_M1540-V2_color=Navy_with_Light Grey
http://www.newbalance.com/exp-pages/exp-pronation.html
I appreciate how New Balance classifies their running shoes according to what you want.
Check this out. This is their custom process designed to help you find the right type of shoe for you:
http://www.newbalance.com/nbrunning/?ICID=RUNHUBFS_PGP_R_2905#cdev-run-shoe-rec-intro