Put berries into a large stainless-steel bowl set over a large pot of gently simmering water. Allow berries to "melt", stirring occasionally, for 3½–4 hours, until they collapse, releasing their juices.
Set 6–8 layers of cheesecloth over a medium bowl, allowing cheesecloth to hang generously over sides. Transfer berries with their juice to center of cheesecloth and draw up sides to form a "purse". Tie closed with kitchen twine, then tie to a long wooden spoon or dowel. Set the medium bowl inside a large stockpot. Rest wooden spoon across top of stockpot, letting purse hang freely inside. Allow berries to strain overnight, letting bowl catch juice.
Submerge six 1-cup canning jars and their lids and ring bands in boiling water; let sterilize for 10 minutes. Remove with tongs, draining jars; transfer to a clean towel to let dry.
Put a large plate into freezer to chill. Discard berry purse. Strain accumulated juice through a fine sieve into a large measuring cup. You should have 4–5 cups of juice. For every 2 cups of juice, measure 1 lb. of sugar (about 2½ cups). Combine juice and sugar in a large pot and bring to a boil ("with haste", says Lee) over high heat. Immediately reduce heat to medium and boil vigorously, skimming off and discarding any foam that rises to the surface, 12–13 minutes. Test jelly by running a finger through a spoonful set on the chilled plate; if the line doesn't disappear, the jelly is ready.
Remove jelly from heat and pour into the sterilized canning jars. Secure jars with lids and ring bands. Transfer filled jars to a canning rack, submerge in a pot of gently boiling water (jars should be covered by at least 1" of water), and boil for 15 minutes. Carefully lift jars from water with jar tongs and place on a dish towel to let cool for 24 hours. To test that jars have sealed properly, press on center of each lid and remove your finger. If lid stays down, it's sealed. Refrigerate any jam that hasn't sealed and use within 4 weeks.