The difference is that lifting weights does provide some cardiac benefit. Not as much as bicycling, but still better than sitting on the couch. I remember my first time doing intense lifting, about two years ago. Though I was not out of breath, I had sweated out something like a pint to a quart of sweat, and I was beat--absolutely dead tired. I was actually shocked by how physically drained I was, even though in comparison to the aerobic exercise I had done at the time, I was barely breathing heavy after lifting.

As for the extra weight being a drain on the heart, I'm not even so sure of that either, right now. My personal experience has shown that focusing on excess weight as a proxy for lack of fitness is an exercise in frustration, and I think it eventually leads to failure down the road for those who believe that the two are equivalent. By the medical definitions, I am morbidly obese. I am over 100 lbs overweight(yes, it's fat). Yet, I bike around 70 miles/week, I bench press 180 with dumbells, shoulder press 140 with same, and I have completed multiple rides over 40 miles and a metric century, and I'll probably do a regular century in the next week or two(my goal for this summer is a 3-4 day 240 mile round trip to VT).

If a doc looked at my current BMI(43) there is no way he would think that I could exercise at the level I currently perform. I know for a fact that most people who have a "normal" weight can't do what I do daily. But by using BMI as a proxy for fitness, I would be considered extremely out of shape--and that just ain't so.