Use only perfectly ripe tomatoes for this dish. They will yield much more liquid to ladle around each colorful serving.
Puree beefsteak tomatoes and 3 tablespoons salt in a food processor until smooth. Line a bowl with double thickness of cheesecloth; transfer puree to bowl. Using a melon baller; scoop out as much cantaloupe as possible into balls; set aside. Scrape out remaining cantaloupe; puree in a food processor. Add to tomato puree. Gather cheesecloth and tie into a bundle. Suspend bundle from a large wooden spoon; hang over bowl to collect the juices for 2 hours (to yield 4 cups liquid).
Core heirloom tomatoes; slice into wedges and rounds. Slice cherry tomatoes in half. Place tomatoes in a bowl; add melon balls, basil, and olive oil, and season with salt and pepper. Toss to combine.
Divide among shallow bowls, mounding salad in center of each. Ladle tomato water around salad and serve immediately.