1) 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.
2) 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.