Wood-type golf club heads include: (a) a club head body member defining an interior chamber; (b) a weight system engaged with a rear perimeter portion of the club head body member; and (c) a connection system connecting the weight system with the club head body (e.g., with the rear of the ball striking face portion). The club heads further may include one or more damping members in the interior chamber to alter the sound and/or otherwise attenuate a vibrational response of the club head. The damping members may extend between the ball striking face and the weight system, and optionally may engage the connection system. The damping member(s) may constitute a foam material compressed within the interior chamber of the club head. Methods of making such golf club head structures also are described.