Boyfriend needs to gain weight

My boyfriend is 22, 5’10”, and weighs around 85-90lbs. Before I get a ton of questions asking why, terrible mother caused him to have ARFID (avoidant restrictive food intake disorder). Look it up if curious. I was wondering what foods he could buy for cheap to help him gain weight. He’s got $30-$40 a week for food. Please give any advice. Thanks:)