I think this is probably a common mistake with people is, ‘I feel like I can walk normally so I should be able to run.’ there is a lot more to running. You need to make sure you have thoroughly strengthened your knee, when you have that layoff after knee surgery; you lose strength in other areas like around your hip and around your ankles.
While you can focus on just your knee, I think it is better to look at strength, holistically. With regards to the weight, exercise bike or riding a bike is a really good way to shed some kilos and not put a lot of stress through your knee, and can be a really good strengthener of the knee in those early stages, when you cannot do a lot of high-intensity stuff.
In terms of running, something we see a lot is a lot of issues with running technique. The way I like to put it is the best runners in the world practice their technique day in and day out, and the rest of us seem to think that we can just go out for a run and it is going to be OK. I think people, particularly after surgery need to spend a lot of time working on their running technique before they go out and do some serious running.