The DVs for food components, such as fat and fiber, which have general recommendations for health but no established RDAs, are based on a 2,000-calorie diet. Most melons are picked several days before peak ripeness to ensure the crop makes the journey from field to table. Although this practice is fine for bananas, it's a problem for melons. That's because melons don't have stored starch that can be converted to sugars, which means they aren't EVER going to get any sweeter than they are on the day they're picked. Water carries the sugar into melons as they ripen on the vine.
Heavier melons contain more water, which means they are probably sweeter.
Look for honeydews that are a manila-folder color, which is a sign of ripeness in this variety. There should be a small amount of give to the rind. Hearing the seeds rattle inside is NOT a sign of ripeness, but rather a sign that a melon is past its prime. The U.S. Department of Agriculture's Agricultural Research Service has recently developed a calcium bath for harvested honeydews that allows them to stay on the vine until fully ripe, yet still withstand the stress of shipment. Growers were expected to start using the process this spring.