Very close. I would make some slight adjustments as follows:

UPDATE dbo.weights

SET

shipweight2 = CASE WHEN shipweight2 IS NULL THEN @weight ELSE shipweight2 END,

--CASE is just to doublecheck -- should always apply because of the WHERE conditions

shipweight3 = CASE WHEN shipweight2 IS NOT NULL AND shipweight3 IS NULL THEN @weight ELSE shipweight3 END

WHERE

id = @id AND

(shipweight2 IS NULL OR shipweight3 IS NULL)