For me it is all about lifestyle choices. I'm going to be fat, but I exercise and try and choose healthy foods, although I am not always good about that. Letting your children eat a lot junk food, and eating a lot of it yourself is not a healthy parenting style. Part of the LLL philosophy is eating foods as close to their natural state as possible. Even before I had a child, I would go through stages where I tried to be make healthy choices in terms of food and exercise.
When my daughter was about two, I switched over to a more whole foods, vegetarian way of eating--lots of raw foods, cut out trans fats and a lot of animal products. I also tried to eat as little as I could and exercise daily, and with my daughter's nursing I ended up losing 50 pounds. I was still categorized as obese, however. Then as I got pregnant and my daughter weaned, I gained the weight back anyway. I want to be diligent about the healthy eating and exercise, but I don't want to lose weight by means other than lifestyle changes that I know I will maintain for the rest of my life.
As far as the comment about ergonomically engineered strollers go, I think the point is that it enables you to increase your speed and get your heart pumping, instead of slowing down because of the slow wheels on a poorly designed stroller. The point isn't to give you extra weight to push, since joggers normally run without pushing anything. And it isn't a good idea to walk and carry handweights anyway although I know some people do it. Better is to increase your speed or incline. Or maybe carry your baby in a sling, which you suggested.
I've done walks with a sling, backpack, regular stroller and jogger stroller, and I try to keep my heartbeat at an aerobic level no matter which one I was using, but the strollers that roll better are better for that than the ones with the crappy wheels that lock up everytime you try and break into a jog. I have to admit, though, that one of the reasons I use the sling is just to give my arm muscles a break. I know I held her longer than I otherwise would. There was no way I would take a walk of any length if I had to hold her solely in my arms the whole time.