The default maximum amount of people that a settlement can have is 10. The Charisma trait is a major factor that affects how many people can be in a settlement. Basically, for each point of Charisma you have, add one to the default 10.
From the Wiki page for Settlements:
Each settlement has a default max population of 10 settlers plus each point of Charisma the character has, which has a base max of 21 before factoring in extra charisma from armor and consumables (the theoretical limit could be much higher once power armor charisma increases are calculated).
I believe that without a recruitment beacon (or with it turned off) no new settlers will arrive at the settlement (unless you send people from another settlement to it). The Wiki does not state otherwise. It also states that if four or more people are left unassigned, no new people with arrive at the settlement until those four plus people are given tasks:
If more than four settlers are either unassigned or assigned to provisioner jobs, no more settlers will arrive on their own.
This is a good way to prevent people from moving in, but it would leave you with 6 farmers only, and four freeloaders in your particular scenario.
The amount of food and water does not appear to be a factor for if people with move in. It's really only for calculating happiness within a settlement. It should be noted that the happiness level will only increase if the food and water level are greater than the total number of settlers in the settlement.