"Balanced diet" is the terminology that's honestly hard to define. Until we have that definition, "a variety of types of food" seems better to me. Here, let me offer a correction:
"Eat a variety of foods, avoiding large amounts of any one thing, and don't overeat; you'll probably be fine."
If your diet is complex carbs with lots of fiber, you probably won't be hungry after ingesting a decent amount of calories. Most people don't do that (myself included), so instead I add in a lot of protein, which also fills me up reasonably quickly on a per-calorie basis.
It's not simply calories that fill you up, so choose the right calories. I can eat a thousand Calories of chocolate chip cookies and still be hungry, but a thousand calories of protein bars or broccoli will usually fill me up reasonably well.
(Actually, I've never managed a couple thousand Calories of just broccoli. I usually do 200-300 Calories of broccoli, but that alone does as much as all those cookies for satiety, so I can then eat a filling-but-sane second dinner and be full+healthy.)
You do something to satiate yourself. Foods high in fiber help with that, to some extent.
It's really a matter of how long we've been overeating. Over time, our body adjusts to accept that as the new norm, or set point for food intake. It just takes more time to sensitize yourself again to less food making you feel "full".
"Eat a variety of foods, avoiding large amounts of any one thing, and don't overeat; you'll probably be fine."