So its a hybrid watermelon tree? Pretty sure its not naturally like this, so maybe you have a farm oriented peach tree or some genetically stimulated apple?

Do a combination of both.

It's generally a good idea to thin fruitlets out, particularly for cultivars that are predisposed to breaking branches due to the weight of the fruit, and for those that are pre-disposed to alternate bearing. If you have questions about a particular cultivar, some research should turn up recommendations or you can ask here, I'm sure someone will have some advice.

Regular pruning back branches so they can handle the load.

Never had branches break...