Certainly on the B737-200 Flaps 2 was a scheduled flap setting for take off and, in certain situations, gave a better RTOW than Flaps 1 or Flaps 5.
When the 737-300 came along I recall that take off performance with Flaps 2 was not scheduled for one reason or another but maybe as the original intention was that pilots could be dual rated on the -200 and -300 and also for "commonality" the flaps 2 position was available.