If the aircraft (737 300-900) is in trim and only minor changes are needed (like say in cruise), you can fly the aircraft with
one finger.
If you are making major changes to flightpath/thrust settings/configuration you need a firm grip. Basically anything which causes the aircraft no longer to be trimmed for the current conditions...
...like you experienced with the steep turns - obviously the aircraft was not in trim to continuously do a steep turn without control column input. If you had trimmed it out for the condition (which we normally wouldn't do during a turn), you could have continued the turn with a light 2 finger grip as well.
By the way a Classic is a 737 300-500. A 200 would be referred to as an "Original" or colloquially as "Jurassic", now a days.
Edit: Was a typo Denti, hereby corrected.