There doesn't seem to be any rhyme or reason to it but I suspect that each point of weight is 1/2 pound. Carry capacity is 300 weight. (Soldiers can carry up to 150 pounds of weight into battle in a full field pack).

In game a carrot weighs .3 weight (~3 oz) - in real life a carrot weighs about 5 oz.
In game boar meat is weight 1 (8 oz) - in real life a dressed out hog provides about 200 pounds of meat (if the Vikings were picky and would only eat the ham 1 hog would still provide about 28 pounds of ham)
A copper ingot weighs 12 (6 pounds) - in real life a copper ingot from the bronze age weighed 63 pounds.
The recipe in game to make a bronze ingot is 2 copper ingots plus 1 tin ingot, which produces 1 bronze ingot. - In real life the copper to tin ratio is 9:1 90% copper and 10% tin.
In game 2 copper ingots and 1 tin ingot are forge welded into 1 bronze ingot. In real life 9 copper ingots and 1 tin ingot are smelted into 10 bronze ingots.
In game it takes 10 bronze ingots (weight 120) and 4 wood (weight 8) to make a bronze buckler (weight 3) - In real life a bronze age buckler weighed about 2.5 pounds (1204 grams) which would be weight 5 in game.