The main point of aa is to make things smooth. I find that it usually turns out better if you aa into the lines, not the outside of them, if that makes sense...The aa should not make the object any bigger.
Also, I think that it usually turns out a little smoother if the aa color is not exactly between the the two colors being aa'ed...for instance, instead of halfways, I go about a third towards the bg color....but this may be person preference.

It's not the best, but maybe this can help a bit. Props for practice!