When I look at a weapons stats, do the numbers I see include my skill point modifiers such as extra damage, or do I have to do the math in my head and add it on?
You have to do it in your head. Stats are always the base stats. (This makes it easier to compare weapons with other players, who have different skill modifiers). So, neither skill effects, kill skill effects, team effects, com effects etc, are added.
Of course this does make it harder for the player to compare the DPS different weapons on specific characters.
I wonder if this is deliberate design (Either to make the game more casual, or to hide potential bugs), or just lazyness/lack of time.
It also leaves open the question if modifiers are additive or multiplicative. (So does +30% skill damage and +10% proficiency damage on a 100 dps gun become 140 dps or 143 dps (100 * 1.3 * 1.1)).