I had to carry two laptops for a trip summer. It is basically a pain and i would not have done it unless my circumstances really aligned the same way again. I ended up having one computer in my normal bag in the laptop pocket then got a cheap backpack and a laptop sleeve case for the other one to spread out the weight. If I had just been on a short trip i would not have done this. Though this was a several month trip and I wanted the benefits of each computer.

In your case it sounds like if you want to keep you personal computing separate from your work comp then get an iPad or something way lighter to carry around to do basic Internet surfing and music/videos.