Unless you have a really long eye-bolt, it's unlikely you could adjust it enough to significantly alter the door's tendency to "drop like a rock." My guess is that the springs need replacing. They're pretty cheap -- $10-$12 each at any home center and fairly easy to replace. Just weigh the unsprung door with a bathroom scale and buy the appropriate weight rating. Replace the cables while you're at it.

Thanks for the response, Mike. I have only had a quick
look at the door while helping the neighbor get a
lost bird out. But the 2 springs on each side, and
the cables, looked really really slack when the door
was up. Are the cable lengths adjustable??

"Are the cable lengths adjustable??"

Follow the cable towards the door.
One cable will go over a pulley and be attached to the door, the other will go to a cable clamp.