Instead of putting a water bottle on the end of the tarp (as Hennessey
suggests), why not just run a line at 90 degrees to the tarp, and its
line going to the ground.
You might be able to use the same stake that pulls out the body of the
hammock, if that does not put to much stress on the stake?
It seems like you could put as much pull on this as a full water
bottle, and it also would prevent the tarp from going up beyond the
length of this line. Only disadvantage might be that the tarp might
be that the tarp would be a little lower to start with?
Putting tarp on its on ridgeline would also help?