Flap 2 in the 737-200 was used extensively at high altitude airports where Flap 1 was a problem with its higher V speeds. I think it was South America where Flap 2 was mainly used. Depending on runway lengths etc, the weights used for Flap 1 and 2 were normally max structual up to around 2000 ft airport altitude.
One advantage of Flap 2 if the choice was available, was a Human Factor aspect, in that the next flap (which was Flap 1) could be selected normally at V2 +15, which left the leading edge devices still extended.
This minimised the danger of someone inadvertently (carelessly?) when conducting a Flap 1 take off, retracting the flaps to up at V2 +15 instead of first accelerating to 190 knots (53 tonnes and below). On quite a few occasions I observed pilots calling for Flaps up at V2 +15 on a Flap 1 take off.