If the engine is not consuming oil or even that much oil and isn't burning it, just stick with original weight if it's just a daily car. If you're consistently doing hardcore racing in the heat of the summer, consider a higher summer weight like the 5w-30 or maybe 40.
Assuming a 6qt sump, if the motor consumes no more than 1 quart per standard 3k mi oil change, probably just leave it alone and continue as normal.
There's no topic more beaten to death in all of human history than oil weight.
I use 5w20 in my 250k mile 5.0 and see no reason to deviate but you can do whatever you like with yours.
I myself use 10W-30, I started with 5W-30 but got some knock on cold starts. After switching to 10W-30, the knocking almost completely went away. I burn about a quart (give or take half a quart depending on how I drive) between oil changes.
A malfunctioning PCV system will cause oil consumption as well as plain old carbon buildup. It seems Valvoline Restore & Protect has resolved the issue of carbon buildup, specifically with piston rings. I'm currently running VRP (on the second oil change now) and so far so good. I'm leveraging laboratory used oil analysis reports to monitor it all.