A machine (1) for filling containers (2) has a carousel conveyor (5) having a vertical axis (6) and in turn having a number of filling heads (7), and an equal number of seats (8), each of which houses a respective container (2), is associated with a respective filling head (7), and is connected to the carousel conveyor (5) via the interposition of a weighing device (9) supported in a fixed position by the carousel conveyor (5). Each seat (8) has a frame (10) , which supports a gripper (11) for engaging a top portion (4) of a respective container (2), and a plate (12) defining a horizontal supporting surface for the bottom of the respective container (2), and an adjusting device (13) for adjusting the vertical position of the plate (12), while maintaining the gripper (11) in a given vertical position close to the respective filling head (7).