put (one) on a diet
To instruct or direct one to begin a specific nutritional plan typically consisting of eating smaller amounts of food, eating (or avoiding) particular foods, or both in an attempt to lose weight or achieve some other health benefit. My doctor put me on a diet rich in red meat and leafy greens for a month to try to bolster my iron levels. I had to put my dog on a diet because it was actually having trouble going up and down the stairs.