What type or class of chemical messenger traveling in the blood would most probably link the brain with the digestive tract and fat cells in the control of body weight?

Hormones.

Explanation:

Hormones may be defined as the chemical messengers of the body that causes the action of the specific tissue. The hormones can be directly transfer into the blood or may be excreted into a duct.

These hormones can travel in the blood that can link the brain with the digestive system and fat cells that control the weight of the body. The abnormal functioning of these hormones can cause a particular disease.

Thus, the answer is hormones.