Old English wecg "a wedge," from Proto-Germanic *wagjaz (source also of Old Norse veggr, Middle Dutch wegge, Dutch wig, Old High German weggi "wedge," dialectal German Weck "wedge-shaped bread roll"), of uncertain origin; perhaps related to Latin vomer "plowshare." From 1610s in reference to other things shaped like a wedge. Of women's shoes or shoe-heels, from 1939. Wedge issue is attested from 1999.
early 15c., "jam in place with a wedge; tighten with a wedge," from wedge (n.). Figurative sense "drive or pack (into)" is from 1720. Meaning "split (something) apart with a wedge" attested by 1853. Related: Wedged; wedging.