I'm new. I looked around various forums and topics but didn't see this listed anywhere. My pool cage has new 20x20 (squares per inch) on the upper levels. It has 14x18 (normal screen) on the sides and heavy 14x18 on the bottom (also called pet screen). My pool is always cooler than the neighbor's (no pool cage) by 2-4 degrees. I'm curious if the finer screen will noticeably slow down the sun burning up FC?

Absolutely. Sometimes you can find a rating of how much light the screen lets through. So if you find that and say it's 70%, then it's is reasonable to expect something in the vicinity 30% less FC loss.

I'm sure the science is not exactly that simple (or the loss is somewhat less) but screens certainly make a difference. AS you have noticed....big difference in temps, too. A relative of mine lives an hour and a half south of Orlando with a screened pool and has to have a heater before he swims.