Running

There may be other options, like training 6/7 days per week to build up enough strength, but if you are carrying a fair bit of extra weight a blended approach of dropping a few pounds combined with a Reasonable training regime is more likely to be successful and not result in over training and either suffering from injury or continued illness due to having weakened the immune system to the point where it can't deal with a cold.

It's like saying that running a 20 minute 5k is possible by sprinting the first 3k and walking the rest and some people will go to prove it is possible, but that doesn't make it the easiest or right way to do it...