I have an '05 WRX wagon with the stock 16" wheels. I drive about 25% highway, 50% twisty 2-lane paved roads and 25% gravel roads.

What are the widest tires I can fit on the stock wheels? What's the downside to putting wider tires on a smaller wheel vs. getting bigger wheels?

Bigger wheels have a few downsides for me right now:
1) I don't want heavy wheels, so most cheap options are out.
2) I don't want to spend a lot of money on wheels.
3) I don't want to explain to the wife why I just dropped a grand on wheels when we have a new baby coming in a month.

 

Don't go wider than stock, just buy better tires.