"old woman," 1570s, contraction of grandmother (corresponding to gaffer, but according to OED representing a different construction).
Entries linking to gammer
grandmother n.
early 15c., from grand- + mother (n.1), probably on analogy of French grand-mère. Replaced earlier grandame (c. 1200) and Old English ealdemodor.
gaffer n.
1580s, "elderly rustic," apparently (based on continental analogies) a contraction of godfather (compare gammer). Originally a term of respect, also applied familiarly; from "old man" it was extended by 1841 to foremen and supervisors, which sense carried over in early 20c. to "electrician in charge of lighting on a film set."