Factory weight depends upon which motor you have My motor (Windsor) was designed for 5w30. The next year they reduced the recommendation to 5W20 for Romeos. If I remember correctly it was to comply with environment guidelines but there are internal differences.
I was a little concerned about this because both oil flow and oil thickness is important. Bearings need a continuous flow of oil to maintain an effective hydrodynamic lift but if the viscosity is too thin, the hydrodynamic lift will be insufficient to keep the bearing from touching the crank so I stayed with 5w30.
I'm a big believer in full-synthetic oil. I switched to it when I installed the supercharger. It is less honey-like so it flows better during cold starts when most of the wear occurs and it doesn't breakdown as much do to heat (it doesn't thin out as much). I have read that you shouldn't use full-synthetic when breaking in a motor. It inhibits break in. The supercharger was installed at the 80,000 mile point break in wasn't a consideration.
According to Bob the Oil Guy we should use the thinnest oil that provides 10 psi per 1,000 rpm. There is a time in all motors lives where increased wear and tear will require a thicker oil. He says the normal progression is from 5w20 to 5w30, etc. If an oil pressure gauge is cannot measure it then the rule of thumb is that if the motor is using a quart of oil every 3,000 miles then the next heavier grade is warranted.
I ran full-synthetic Quaker State 5w30 for many years but switched to full-synthetic Mobile 1 0w30 because it had better cold start protection.
Then I started reading articles about how ZDDP is important to protecting motors. Since the 1940s when oil had .03% or 300 ppm the recommended level of ZDDP constantly increased until it hit 0.10% or 1,000 ppm in the 1970s. But ZDDP hurts catalytic converters. Many engineers said that 800 ppms (0.08%) was sufficient. The Mobile 1 0w30 I was using only had 650 ppm so I switched to full-synthetic Mobile 1 European blend 0w30. It had 1000 ppm.
I ran that for a lot of years and I change oil every 3,000 miles. Somewhere around the 150,000-160,000 mile mark I noticed it was using half quart or so of oil between oil changes. When it it reached 9/10th quart I switched to Mobile 1 full-synthetic European blend 0w40. My car is at 215,000 miles and it uses no oil between oil changes.
I did something else. There was a post a long-time ago about a guy running prolonged high rpm pumping his oil pan dry. The recommended oil capacity for my car was 5 quarts. Romeos are 6 quarts. The oil pan will easily hold 6.5-7 quarts with out any interference with anything so I started running 6.5 quarts. It looked like I was overfilling it so I bought either a cobra or newer GT dipstick. It is shorter and 6.5 quarts hits the fill mark exactly.
My car has 215,000 miles and the last 135,000 were supercharged. Its still running strong and it uses no oil.