And if she checked you YOU would be the one aging very slow, since she is standing still and you are moving fast.
You are still thinking in terms of absolute motion "you're moving". You are not moving, you can only compare your speed with someone else's.
But if he accelerates then things are quite different, and much more complicated.
I used to think about it as I explained in my previous comment. But now that ars is making these comments, it seems like I'm grasping something new.
This FIRST thing to remember is that you can only measure speed by comparing with something else. There is no such thing as the concept of "I am moving", but rather "relative to them I (or they, it's interchangeable) are/am moving".
Now when you compare speeds you can also compare clocks, and the same principle applies - you can only measure time by comparing to someone else.
And if you would stay, say for a minute in that speed and go check on the standing person, you will perceive that she is aging very fast.