For an aircraft to remain in level flight, it must generate lift force that is exactly equivalent to its weight. However, modern airliners lose a lot of weight when they are in cruise flight in the form of fuel burning off. Therefore, it stands to reason that to remain in level cruise while the aircraft's weight reduces, the lift the wing generates must also reduce. How do airliners accomplish this? They generally don't adjust their cruising speed, and the wing geometry itself doesn't change (purposefully), so I assume that airliners fly at reduced angle of attack to remain level?
Edit: It's been made clear in the comments that there are multiple ways this could be accomplished. I'm curious how exactly it's done by airliners today.