Du leder efter en kumulativ sum. Noget som dette:
select t1.*,
(case when cumecap <= t2.item_amount
then t1.capacity
when cumecap - t1.capacity <= t2.item_amount
then t2.item_amount - (cumecap - t1.capacity)
else 0
end) as allocated_capacity
from (select t1.*,
sum(t1.capacity) over (partition by bag_type order by bag_id) as cumecap
from t1
) t1 join
t2
on t1.bag_type = t2.item_type;