SQL Server 2014

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-- Sample data
declare @Customer_Item table (CustomerId int, Amount money, ItemId int
	, ItemPrice money, isActiveStore bit, [Priority] smallint)
insert into @Customer_Item values
	(1, 1000, 1,  100, 1, 1), (1, 1000, 2,  200, 1, 2),
	(1, 1000, 3,  300, 0, 3), (2, 5000, 4, 1000, 1, 1),
	(2, 5000, 5, 3999, 1, 2), (2, 5000, 6,  500, 1, 3)

-- Customers table to update
select CustomerId
	,  Amount - Max(SumPrices) as NewAmount
from (
	select *
	, ( select sum(ItemPrice * isActiveStore)
		from @Customer_Item
		where CustomerId = civ.CustomerId
            and ItemPrice <= Amount 
			and [Priority] <= civ.[Priority]) SumPrices
	from @Customer_Item civ) Customer_Item_Extended
where SumPrices <= Amount
group by CustomerId, Amount

-- Items table to update
select ItemId
	,  case when SumPrices > Amount
  				or ItemPrice > Amount
				or isActiveStore = 0
		then 'skipped' else 'subtracted'
	   end as NewItemStatus
from (
	select *
	, ( select sum(ItemPrice * isActiveStore)
		from @Customer_Item
		where CustomerId = civ.CustomerId
			and ItemPrice <= Amount  
			and [Priority] <= civ.[Priority]) SumPrices
	from @Customer_Item civ) Customer_Item_Extended

CustomerId	NewAmount
1	700.0000
2	1.0000

ItemId	NewItemStatus
1	subtracted
2	subtracted
3	skipped
4	subtracted
5	subtracted
6	skipped