1) To roll or turn something over.
Thoresby had ‘welt’ meaning to overturn a cart or wain and an amusing by-name had that exact meaning: 1263 Robert Weltecarte, Harewood. To 'walt ovver' has survived in the dialect, and is used when a person turns his foot over, or loses his balance when seated.
2) In shoemaking, the welt was a strip of leather that joined and was attached to the sole and upper leather, holding them together. The verb meant to repair or renew welts and this was seen as a cobbler’s task not a shoemaker’s.
1582 and to capp and welt both old bootes and shoes with new blacke leather, York
1589 the cordyners ther servants and apprentices may sole shoes and botes … so they do not welt or clowt any shoes bootes or other wayr, York
1773 George Shoes Soald & heelespecht and Capild and Welted, Meltham. More generally, the verb and noun referred to furnishing a garment with a border or hem of material: 1540 my blake gowne of cloth weltede with velvet and faced with bogge, Whitby
1545 to my mother one gowne walted with velvett, Collingham
1559 a blacke clothe cloke with welts of velvet, Hipswell
1572 one overbodie of satten of bridges, and welted with cremyson velvett, Skipton Castle.