I carry two camera bodies most of the time. Mostly my K-5 with battery grip and my smaller K-m, but sometimes my K-5 and K10D....both with battery grips. I have carried all three at times, but not very often. Too hard to keep three...from clanking together....when walking around. Tiring too for a senior citizen.
I'm bigger (6'3" , 240 lbs.)....but as mentioned before...I'm older and I, like the OP, also have a bad back. I know what type of physical movement throws my back out...so I'm careful to avoid that kind of movement.
When I go on photo day trips...I carry all three...and also my small Canon G 12. Then I usually have them packed into the back seat of my car. The K-5, has the 150-500 Sigma, the K10D...either the 55-300 or the 10-17....or the 12-24. The K-m usually has the 70 or the 50 macro.
Be prepared as the Boy Scouts say.