The amount of Resources that your Defensive Units can collect from a Hamlet depends on their total carrying capacity. Moreover, the speed with which Resources are gathered at Hamlets depends on the Level of the Lost Art “Dominion”.
The "Hamlet Gathering Speed Boost" bonus is applied only to Hamlets that were captured after the item was applied. If the Hamlet was captured before the activation, you won't benefit from that bonus.
To begin with, the maximum number of Hamlets that can be held at one time is three. Upgrade the "Maximum Resource Sites" Skill at your Obelisk of Power to increase this number.
The number of Hamlets you can hold at the one time is also dependent on the number of Carts you have. To check the number of Carts available to you, tap the Cart icon in the upper right corner of the Capture window.