Congrats on deciding to do something good for yourself. As far as weights go, don’t worry about it, healing is more important. The worst thing you could do right now would be to tear open that incision and end up laid up in the hospital for god knows how long. How much fat do you think you’ll lose laying in bed (not to mention it’d probably be mentally and emotionally devastating to have something so good turn so bad).
If your doctor says it’s ok to walk on the treadmil why not get outside and do it. Go out and buy a good supportive pair of walking shoes, or better yet hiking boots with some ankle support, and get outside. Not sure where you’re located but it’s summer in the northern hemisphere and prime hiking season. Keep hydration in mind, especially if you’re somewhere down south where it gets really hot, it’s really easy to get dehydrated and sick, especially if you’re on the heavier side. It’s a lot more exciting than walking on a treadmill and can easily incorporate other activities. You can pack a lunch in a pack and hike out for a picnic, eat and relax for a bit, then hike back. Or grab a nature book and some bug spray, head out in the woods, and try to identify the different trees and plants, learning and exercising at the same time WOW!
Not only will this help you lose fat, but it’ll help build endurance for when you finally can get into the gym and start lifting.
Another option may be to start working on flexibility. Again, be careful of that incision, but starting a good stretching routine now will help get your joints, tendons, ligaments, etc… used to moving and help a lot when you finally can start doing some resistence exercise.
Hope this helps,