A motion stabilizing system includes at least one stabilizer coupled to a structure in a water environment. Each stabilizer includes a tension member, an open-ended container having a set of holes, and at least one one-way valve associated with the holes. For each stabilizer, the tension member has a first end and a second end with the first end coupled to a portion of the structure and the second end disposed in the water environment; the container is coupled to the tension member and is suspended in the water environment; and the one or more one-way valves are operable to seal the holes when the portion of the structure moves away from the container and unseal the holes when the portion of the structure moves towards the container.