We just used cotton garden twine and yes, we tied it to the top of the fence. The weight is mainly on the top of the twine where it is secured to the fence top. We trained the vines at first to go up the twine and then they just took off. For melons, squash and heavier crops, I would use two pieces of twine wound together and the slings for extra support.
Any of the vine crops will work this way. The vines get much larger when the crops are grown this way. The heavier the crops get, the thicker the vines get in return. We had several types of zuchini and cucumbers and even tried cantaloupe one year but it was too cool for them to get much size on them, we have a shorter growing season.
I have even see pumpkins grown this way :D:D:D