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If you've got a calibrate oil pressure and temp gauge (the oem dash gauge is NOT calibrated enough) you can do your experimenting and MAYBE NOT harm your engine.
Thinner (lower weight) oil flows better. Thicker Oil (higher weight) protects better.
Usually the owner's manual has a recommendation based off the temperature, use what is recommended by the manufacturer for the temperatures you drive in. If you have a graph or range that you end up falling into that two different weights of oil will work, choose the thicker oil for better protection.
You only need thinner oil for cold start-up, to make sure it flows.
Yes, thinner oil can give you better fuel economy, but we are talking a fraction of MPG here, at the cost of better protecting your motor. As well, the more worn an engine, the worse the mileage it gets. So you can save 1/5 mpg now, and then lose 5 mpg 100k miles from now. OR you can lose that 1/5 mpg now, and only lose 1 mpg 100k miles from now. Take your choice, I'd recommend choosing the weight of oil that will protect the motor the best, NOT give you an extra fraction of a mpg at the cost protecting the motor less.
Remember the manufacturer has CAFE to meet, been given all sorts of incentives to encourage you to save energy and they would prefer you buy a new car in a few years, they are biased toward recommending the lighter less protecting oil that gives a fraction of MPG.
10W-30 oil means, 10 means @ 0°F the oil has the same viscosity as standard straight "10" weight oil, W means it has passed a winter flow test of flowing out of the can at -20°F, 30 means @ 200°F the oil has the same viscosity as standard straight "30" weight oil.
NO, the oil does NOT get thicker (more viscous) as it gets hotter, 30 weight oil is thinner at 200° than 10 weight oil is at 0°F, it means the oil thins out at a slower rate as it gets hotter, than straight weight oil.
The oil achieves that with a bunch of additives, and the additive that does the multi-viscosity are polymer chains that coil up cold and expand when hot, these additive are the first to burn and coke up the oil and make sludge.
SO, if you can do it, the closer the bottom and top range of the oil, the less additive in the oil, thus less additive to burn and create deposits and get the motor dirty. i.e. 10W30 is better than 5W30, because of the narrower spread.
Use what the manual says, for the temperatures you drive the vehicle, if you fall into a range where you can choose, choose the higher viscosity and then the viscosity with the narrowest range, if the temps you drive at support it.