Cockcroft-Gault multiplies by body weight because weight stands in for muscle mass, and muscle mass is what produces creatinine. Adipose tissue produces very little. So in a patient carrying a large amount of fat, feeding actual weight into the equation credits them with muscle they do not have and overestimates clearance — which, for a renally cleared drug with a narrow margin, means a dose that is too high.
Ideal body weight corrects that by estimating what the patient would weigh at a healthy build for their height. Adjusted body weight sits between the two, on the reasoning that fat tissue is not metabolically inert and contributes something. Which one applies is a decision, and this page exists to make that decision visible rather than silent.