Installed a brand new Victory range hood, I ran new 6" pipe that goes from the kitchen, through the attic to the roof vent. I installed a new roof vent exhaust to accept the larger pipe diameter than what was there before which was 4".

I have a dampener on the roof vent and also immediately above the range hood.

Every time I turn my vent hood on, water comes out from the weep hole on the base of the motor. I highly suspect this is condensation from the cool house air meeting the warm attic air and outside air.

What options do I have to prevent this from happening, or have I done something wrong?

Is the exhaust pipe double walled? Insulated?

This.

Insulate your exhaust pipe?

Disco Stu said:

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Is the exhaust pipe double walled? Insulated?

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It is not, this is just single wall rigid pipe. If I'm honest I didn't know they made a double wall insulated pipe. What are my options now?

Duct wrap your pipe.
It doesn't carry a great amount of heat. Treat it like a normal a/c duct.

Agree with all above which would indicate a poor baffle at hood allow cold air up into the attic pipe, then condensate down (at least) pipe exteriors.
So leaves little more to explore
BUT
this does not appear to be a Broan or better roof vent, perhaps a Master Flow from Home Depot.
Some of these ended up on the shelves abused and some flaps/dampers have been reported as not closing all the way ... something I'm sure you tested, judging from the install perfection in photos.

They make weights and magnets for baffles to insure a tighter closure.

All that's left is revisiting the roof, thinking uphill crickets, bigger vent overhangs, anti-splashing, more sealant, etc. which would be a surprise if any a solution here.

That's all the fishing most have done in solving this perpetual problem.