The Humakti is a special case (they can get bonuses to a specific weapon via a geas, so a close combat 1W Humakti might be +5 or 6W with Greatsword). You can apply the logic generically (but I'd advise making CC +3 hp to increase and each specialization +1).
My preference is to stick with the rules as written. So far we have had 3 combats in two sessions followed by two sessions with no combats (and they were the most fun). Making CC +3 hp to increase would make it prohibitively hard to improve (i.e., it would cost +2 or +6 hp to get an increase a lot of the time). However, if combat features more strongly in your campaign you might want to change.
Thom
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