I used the hand cannon telemetry and turned in two bounties and barely got any XP for it. I did the same today but had the auto rifle telemetry and received the XP this time around. Not sure if there was an issue with the hand cannon xp not registering.
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Yes the level of rarity of the weapon affects the total Exp needed to level, plus your own account level with regard to weapon class. Example if you have rank 3 auto rifle grimoire accomplishment you gain more auto Exp then. Check your grimoire in inventory/primary/hand cannon. See what rank you have accomplished.