Shoe choice is actually a factor, but honestly, I'd approach the problem differently. The key thing is that your knees don't get overloaded from the start - when you're jogging with extra weight, the impact is just significantly higher. Maybe you're making it harder for yourself than necessary if you jump straight into running. A lot of people underestimate how effective walking, swimming, or cycling are - you avoid all those tons of impact per step and still build endurance and lose weight.
If you really want to run, then you do need decent shoes, not some worn-out pair from years ago. But not because "overweight shoes" exist, rather because good cushioning and stability matter. Get advice when you buy - a lot of sports stores do gait analysis, and that quickly shows whether your foot turns inward or if something else is off with your running. That's way more useful for you than guessing on the internet.
And yeah, like someone mentioned before: if your knees really hurt, you should get that checked out before you start training without a plan. An orthopedic checkup might save you months of problems down the line.