The extensible leash system comprises a rope and a leash extending from the rope. A weight system including an incremental weight device is suspended to the rope and has a first, second, third and fourth weights mounted therein. There is also provided a mechanism for raising the first, second, third and fourth weights with the rope in sequence according to a first distance interval along the rope between the first and second weights, according to a second distance interval along the rope between the second and third weights, and according to a third distance interval along the rope between the third and fourth weights, wherein a relation between the weight extents of the first, second, third and fourth weights, and the first, second and third distance intervals represents an exponential increase in a restraining action on the rope and the leash.