Firstly, 3.7kg is light, and the original flywheel is around 6.5kg for the sporty 4A-GE. Some standard cars have a 12kg flywheel. But this is the static weight. If we are engineers, we are interested in the Moment of Inertia. Because the moment of intertia (resistance to acceleration) can be different in 2 flywheels both of the same static weight. But this is getting too technical...
Advantages of a very light flywheel:
Faster acceleration (less rotating weight)
Quicker 1/4 mile
Higher dyno figures on some dynos, the ones that measure acceleration
Disadvantages of very light flywheel:
Will be harder to drive up a steep driveway
Harder to drive in stop-start traffic, will stall more often
Engine revs will drop very quickly the moment you lift off the throttle.
Dyno figure on most dynos will not be any different.
Engine tune at idle is more critical, otherwise may run rough.
One disadvantage of the thin chrome-moly flywheels Toda and the like made, is that they can overheat easily and distort. But if a cast iron flywheel is lightened that much it may explode. You can lighten the stock flywheel alot, just maintain a 12mm or 1/2" thickness as a general rule of thumb. (Don't hold me responsible for this).
I saw a nice MkII Escort with a fully worked motor do well at this hill climb. Had it reving towards 9000rpm all the way. But when he got to the really tight corners, one lift off the thottle brought the revs back to idle and it was hard to get going again. Flywheel was probably a bit too light.
You probably don't want a very light flywheel with turbo. The inertia of a heavier flywheel is used to get boost started.