From the sentence you posted, "Heavy-looking" is referring to someone who is chubby or possibly overweight looking.

What does it mean if a person is heavy?

heavy Add to list Share. Something that's heavy weighs a lot, either physically or emotionally. ... Bulky, substantial things are heavy, and you can also describe people as heavy, especially if they're big-boned and carry a lot of weight.

What does heavy mean in British slang?

Heavy is defined as a somber role or the role of a villain in theatre or is slang for an influential person.