Learn Dutch: Hij eet zo weinig mogelijk. - He eats as little as possible.

In English, you say "as little as possible," repeating the word "as." In Dutch, this specific construction always uses the pattern zo [adverb/adjective] mogelijk. You don't use als here. For example, "as fast as possible" is zo snel mogelijk, and "as little as possible" is zo weinig mogelijk.

Could I use klein or een beetje instead of weinig here?

No, because they mean different things. Klein means "small" in physical size. Een beetje means "a little bit" (a small but positive amount). Weinig specifically means "little" in the sense of "not much" or "few." Since he is minimizing the amount of food he eats, weinig is the correct word.

Is mogelijk related to the verb mogen?

Yes! Mogelijk translates to "possible." It comes from the root of the verb mogen (to be allowed to, or "may"). The ending -lijk turns it into an adjective, similar to how we add endings like "-ible" or "-ly" in English.

How would I change this sentence to say "He eats as little meat as possible"?