Just looked up Grandmother in the Only Etymology Dictionary. It says:
early 15c.,from grand (adj.) + mother (n.1),probably on analogy of French grand-mère. Replaced earlier grandame (c.1200) and Old English ealdemodor.
and under Granny:
1660s,according to OED,most likely a diminutive and contraction of grannam,shortened form of grandame,rather than from grandmother.
and under Grandfather,it says:
early 15c.,from grand (adj.) + father (n.),probably on analogy of French grand-père. Replaced grandsire and Old English ealdefæder.
