"but I need to drop some weight and get in better shape before I go on a trip like that."
You couldn't be more wrong, Kathy! For better and for worse, the mentality in China is like ours back in the 1850's. If there is something out there, then hey, let's build a road to it! Not the Chinese mindset to make do with trails plus four days of hard slogging -- like in 'poor' Nepal.
On the Chinese side, you can fly -- or take the very nice, air conditioned sleeper train -- to Lhasa, Tibet. There, spend a few days to enjoy the culture, acclimate yourself, and sign up for a jeep tour to Everest Base Camp. Your jeep will take you to within 4km of base camp. There, you switch to the park's electric minivan, and it will deliver you right to your tent! The only walking is the two or three steps getting off the van and into your tent. They even serve hot noodle soup up there!
When I was there, I knew I would never forgive myself riding all the way to camp. So at the junction where people switched to electric minivans, I chose to hike up the final 4km instead. I really, really enjoyed that short hike, and was quite pleased with myself that I didn't feel winded at all. But the good thing is that everyone has an option to hike or not -- and still enjoy the incredible view that is Mt. Everest.