The claims were made in an affidavit made by Smith's former nanny Quethlie Alexis in the Bahamas on December 4 last year.
"Ms Marshall (Smith's real name) was obsessed with making sure that her baby was 'sexy'," the document, obtained by website TMZ.com reported yesterday, reads.
"Ms Marshall knew that the correct amount of baby food was three ounces every three hours ... Ms Marshall insisted that the maximum I was to give was 2.5 ounces (70.8g)."
Ms Alexis claimed that Smith, who struggled with her weight throughout her life, enforced the order by "making sure the baby monitor was kept on all the time".