Trap:
Initial tick uses damage of current bar and penetration of cast bar. DoT uses damage and penetration of current bar for the first tick and doesn't change after that.
Edit: Stats are calculated when arming instead of first tick, as the poster above said.
Poison Injection:
Initial tick uses damage and penetration of cast bar. DoT uses damage and penetration of current bar for the first tick and doesn't change after that.
Trap:
Initial tick uses damage of current bar and penetration of cast bar. DoT uses damage and penetration of current bar for the first tick and doesn't change after that.
Edit: Stats are calculated when arming instead of first tick, as the poster above said.
Poison Injection:
Initial tick uses damage and penetration of cast bar. DoT uses damage and penetration of current bar for the first tick and doesn't change after that.
Regarding PI. Wrong. What Izaki said is right. Every tick of the DoT is based on your current stats.
Poison Injection calculates its tick every times before it happens, so it will be dealing more damage if the weapon damage is higher on the bar you've swapped to.
Lightweight and Rearming Trap both work the differently, they benefit from the stats of the bar they arm on and don't change their damage when you barswap. So you can: put a Trap down and bar swap, when the Trap arms, it will benefit from the higher stats on the front bar.
(BTW: don't use Lightweight trap... its crap compared to Rearming)