I used to get terrible upper back/neck pain and headaches from a full backpack. Just something about it, no matter what backpack or how it fit. Not to mention a gross sweaty back during the warmer months. I switched to a messenger bag and never looked back. My first and current one is from Fossil. If/when it comes time to replace, I will be looking for a ClaireChase computer bag (VERY expensive from the retailer, but much better prices on ebay). Factoring in the years it will last, and the heavy daily use I will get out of it, the cost per wear works out to be pennies. Definitely worth it. Fossil's leather quality is hit or miss, but all of the CC I have touched has been superb.
No help to the OP, I realize, who wants leather alternatives -- I'm just a fan the way good quality leather wears.
But anyway, I'm sure the asymmetric weight isn't GOOD for your back, but I switch sides pretty regularly and haven't had any significant issues.