You're getting tired of the size/weight of an APS-C camera and lens, but are considering full frame? The Sony is small by FF standards but it's not compact by any means, and any 2.8 zoom is going to be big.
Main question is why do you want a full frame camera? There should be some more compelling reasons that "cause it's better". Usually because you need better low light performance or you tend to crop like mad and so need lots of resolution. In fact besides those two reasons, I can't think of any other good ones.
I have a Canon 70D and I would like to go full frame sooner or later. I do crop a lot sometimes (but this is also because I don't have a tele photo lens yet). I also use my living room as a home studio at times and only rely on natural light. Your reply made me think I am the perfect candidate for this upgrade.
Do you agree? Sooner better than later?