The first thing to say about tavern clock weights is never to assume that the weight that comes with a clock started life in that clock. The image shows some shapes that you might encounter (including some modern unfinished castings) but there are others including rectangular and cylindrical, although the latter is the least likely to be correct as many are from longcases. Weights were mostly made of cast lead and the better quality ones are in a brass casing. 

Occasionally additional lead has been added to a weight to make the clock run and in extremis it is the case that a 16-20lb weight will be found. Tavern clock movements when properly serviced will run on 9-12lb weights.

Movements in smaller cases with shorter trunks struggle to achieve run times of 8 days without re-designing the wheel train. In order to overcome the problem weights will be cast with a slot in the weight itself so that the pulley sits inside the weight.