2003 Ford Expedition burning a lot of oil?

I have a 2003 Ford Expedition XLT with a 4.6 Triton engine with 191K miles. I noticed around 175K miles that I was losing about a quart of oil per 1K miles, sometimes losing more oil. There's no evidence of a leak anytime I park, even overnight. I notice gray smoke sometimes out of the tailpipe upon starting, but not every time. I do not notice any smoke upon acceleration. Ford specs for this vehicle call for 5W-20 oil, which I have used since I bought this truck when it had 47K miles on it. Oil and filter changes every 3K miles. PVC valve was recently changed when I noticed the issue. I'm not sure what brand the PVC valve is, but I purchased from the Ford dealership. I recently went up to Quaker State Defy 10W-30 with no improvement. Any suggestions of what I can do? Would it hurt anything to put a higher weight oil in? If so, what is the max weight I should use?

The problem is most likely your piston rings. If there's no oil leaking from the engine and you have noticed the smoke, then you are getting oil into the combustion area of your cylinders. Higher weight oil won't do you any good at all, most likely it will hurt your engine. It's engineered to operate at the recommended weight, any higher and you run the possibility of starving your bearings and journals of oil and setting yourself up for a disaster. The PCV valve has little to do with it, it's there to let the blow by from the pistons out and relieve the pressure in the crank case. It's probably just coincidence that you noticed it then. A ring job is going to be big $$$ at the dealership. You may even want to consider a junk yard donor instead of their cost. The good news is that if it's the rings, you can prolong a complete failure for quite some time as long as you maintain adequate oil levels. The risk is that you burn off too much and starve the engine of needed lubrication and things fail, con rods, piston pins, crank bearings… And if the worn rings get too far out, then your power and fuel economy suffer severely as there's less compression from the combustion gasses because they flow around the pistons.

Worn piston rings and cylinders, engines needs a re bore and new piston rings.