Difference between TAKE UP and TAKE ON (= to begin to do something)

Well. Take up means- 1) to start being keen on smth, to begin doing smth on regular basis. I took up tennis. I wish I took up mathematics. And second relevant definition is - to consume or occupy . The books on finance take up three shelves. All my time is taken up with looking after kids.

Whereas take on means to begin to have or exhibit. In the dark, the teddy bear took on the appearance of a fearsome monster. Another definition is to - assume responsibility for... I'll take on this project if no one else wants to take it. And I guess , another appropriate meaning of take on is to attempt to fight or compete with. I don't recommend taking on that bully ,since he is bigger than you .

Therewith, my answer to your question is

You look exhausted. I think you've taken on more than you can handle.

Because it kinda means to assume responsibility for. I guess you see what I mean.