My guess is BE. Out of the BE and Circle H stuff I have, the BE stuff seems more likely to have a lighter maker stamp, that is prone to removal. Both of them have the cross-hatch knurling.
And...found in the '39 catalog, as an 11 pc midget set. Looks to be past the time where they did the folded steel holder, and moved to a box. Pg 3 (really first page with items on it), should be 7/32-7/16 in 12 pt, 1/4 and 5/16 in 8pt, and a Flex "T" handle with crossbar. Looks like four.cycle's was the step up, holding 16 pcs.