If you can touch the ground with both feet flat while mounted, your saddle is way too low.
Depends on the bike. I have an Electra, and they're designed specifically so that you're able to put your feet flat on the ground when you stop-- which is why I got it, since at the time I hadn't owned a bike in 20 years and was terrified of falling over.
That said: my terror of falling over was largely unfounded. I also rode a bike-share bike around the Chicago Loop* while I was still working down there, and after a few weeks of adjusting the saddle so it was super-low, I worked up to having it at a proper height.
Basically: I'm not worried if you start off with the saddle low. As you get your confidence back, you'll start tinkering with how to get the best ride and you'll feel better about moving the saddle higher.
And for the record: I'm overweight, and biking helps me feel a lot better about myself. I might be fat, but I'm hossing my own freight around-- which cannot be said for the skinny folks in cars!
*
In retrospect, diving directly into Loop traffic-- which sounds like an awful idea-- turned out to be the best way to get back on a bike, ever. There are a lot of people on bikes, especially now that we have bike-share, and not only were the drivers already watching for bikes, they were already driving pretty slowly due to traffic.