Mesh tarp sleeves. Katharina at Mountain Goat (outdoortrailgear.com) makes them custom for no extra cost. Just let her know the size of your tarp. They have sleeves for your line or other storage and because they're mesh the tarp will drip dry and weigh less.
Of course some go to a Bishop bag approach. Both have merit.
“The word 'hammockable' (describing two trees that are the perfect distance apart between which a hammock can be hung) is not in the dictionary, but it should be.”
― Dan Kieran, The Book of Idle Pleasures