I've had the same problem with this pitch. Because it is open on only one end there is no circulation and so moisture rising from you (or from the ground, which happens when the ground is moist and less cold than the air) condenses on the underside.

The fix is to make sure that the tarp is off the ground in every direction. Just a few inches might be enough.

To handle wet tarps (either from rain or condensation) I always carry my lightload towel. A few minutes in the morning is all it takes to dry the tarp.