Bedwyr is a Dwarf from the Copperhead region of Lancre. He works in a mine, appreciates a well-seasoned rat prepared by his wife Bleddyn, and respects the old ways. However, he openly acknowledges his wife is of a different gender and female, even to the extent of describing her as "his wife", and is aware he has daughters and nieces as well as sons and nephews. He even sends his children to what, in context, is a fairly newly established village school in Lancre Town.
Trouble happens when the Deep-downer Grags come calling. Bedwyr is forced to take fairly decisive action to prevent them burning down the clacks tower. this enrages him, as his niece works on the clacks down Quirm way.
Bedwyr is the original Welsh spelling for the knight who, in the later Arthurian mythos, becomes Bedivere. (Bedwyr ap Pedrod, also known as Bedwyr Bedrydant - "Bedivere of the Perfect Sinews"). It was also used in Monty Python and the Holy Grail by Tim The Enchanter:
"To the north there lies a cave -- the cave of Caer Bannog -- wherein, carved in mystic runes upon the very living rock, the last words of Ylfin Bedwyr of Rhagedd [boom] proclaim the last resting place of the most Holy Grail."
It is interesting that the naming convention in Lancre bastardises Norse and Welsh forms: in a name otherwise impeccably Welsh, you might have expected Bedwyr ap Bedd. rather than Berwyn Beddsson.
Bedd in Welsh means "grave" or "tomb", btw. It persists in placenames like "Beddgelert" (Caernarfon, Gwynnedd) or "Cefn-y-Bedd" near Wrexham.