1) Of uncertain meaning but possibly a hanging board or shelf on which cheeses could be kept whilst they matured.
2) A short sword, originally intended to hang from the belt.
1512 Item ij batell axis ... ij swords and a dager and a hynger iijs, York
1535 with his Wodknyf or hanger and dagger by his syde, Beverley
1698 with brown clothes and a hanger by his side tip’t with silver, West Riding. It could also refer to the loops on a belt from which the sword was hung, sometimes richly ornamented: 1612 the girdles and hangers to be of blacke leather, and not such girdles as are called Northerne belts, Scarborough
1616 furnashed with ... a sworde girdle & hyngers, Brandsby and more generally to hooks from which items could be hung, as in a kitchen: 1634 a shelf and the hingers, Elmswell.