It does, go to Grimoire score check inventory and go to primary special and heavy and see
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Look at your inventory before and after you get a weapon like say pocket infinity, you'll see it doesn't change
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No it doesn't, when I turned in the bounty for invective and received the weapon for the first time, I checked my grimoire and it didn't increase. Not all cards give you score, if they did it would show it on the card indicated by the +5. Got gjallarhorn last Friday and the same thing happened. Look it up