Disclosed herein are some embodiments of a golf club head with a tapered sole weight. One embodiment comprises a golf club head comprising a sole weight; and a body comprising a sole comprising an exterior sole surface, wherein a sole weight port is formed in the sole. The sole weight port can have a port top comprising an interior port top surface and an exterior port top surface, wherein the interior port top surface has a taper of plus or minus approximately 1-89 degrees with respect to the exterior port top surface. The sole weight port can comprise a weight-receiving cavity that engages the sole weight. Other embodiments for related club heads and methods are also disclosed.