Technically, I believe that the first part of weave is a Pass Thru (or Left Pass Thru) type of movement, with a slight turn toward the shoulder being passed. Then, those coming into the center Pass the other shoulder, while turning 1/4 in that direction. Dance-wise, those coming into the middle almost always hook hands to Arm Turn 1/4 as in Pass The Ocean from Facing Couples.
The use of hands, of course, makes it easier for the dancers to execute the call, in fact most dancers use hands for both parts of the call. The standard cheat definition for Weave is an Any Hand 1/4 Thru.
When I first learned Weave (and Scoot & Weave), it was explained to me that it was a no-hands movement just like Weave The Ring.
Lee Kopman wrote Scoot & Weave, Weave, and Turn & Weave in 1974.
