How many watermelons should you grow/keep per vine and what to do with secondary vines? Will removing the secondary vines and/or only growing 1, 2 or 3 per main vine produce bigger, sweeter, better melons? Will leaving everything alone make smaller melons?
Watermelons Per Vine
A lot of that depends on the variety of watermelon you're growing. With the larger varieties, I've found it best to take all but the strongest plant for a larger melon. Leave the secondaries, they are needed to help get nutrients to the whole plant.
The number of melons on the vine with the smaller varieties really doesn't effect the size.
And taste is governed by the availability of water and other nutrients.
Melons are heavy feeds and I side dress with compost weekly for good results. Nothing tastes better than a home grown watermelon ^-^