It doesn't really look like blight to me, it's missing the characteristic yellow and brown blotches on the leaves. Perhaps its some kind of viral infection.
If you pull them out be sure to get as much of the root as possible and don't compost any part of the plant. Throw them in the trash.
For next year plant them further apart, not only will that reduce the chance of disease but you'll have bigger, healthier plants. And don't let any vine or leaf touch the ground. Its a good practice to strip all leaves from the bottom 12" of each plant. Also remove all dead leaves and branches ASAP.
Good luck and let us know how it goes.