Agreed - giving them room is the best thing you can do.
If you still want to stake them though, here's what you have to do. You need a strong staking support, as the fruits get heavy. When a fruit develops and starts growing larger, you need to tie it off to the staking frame so that the frame supports all of the weight of the fruit, not the plant. I did this last year with Butternut squash using a pair of giant sized panty hose. I cut them into sections, made little mesh bags out of them, put the squash in the bag, and then tied the top of the bag to the frame, being sure that no extra pressure or tension was being placed on the plant. It worked like a charm.
This same approach can be used for melons too if you's like. It is more work, but I found it rather amusing seeing fruit wearing panty hose