I think the "exactness" of the statement depends on if you are a mathematician or a layman.That's not exactly true. If you can stroke a heavier cue at the same speed as a lighter cue (which isn't as easy as it sounds), the cue ball speed will be significantly faster with the heavier cue. See the discussion and plots on pages 9-11 in TP A.30.
The type of tip can also make a significant difference. A phenolic tip can provide about 17% more break power/energy than a typical medium-hardness leather tip (see the bottom of page 10 in TP A.30).
Regards,
Dave

I think I understand the graph on p.9 of TP_A-30, but there is an equal chance I don't.
It appears that there is an increase in cue ball speed for a heavier cue, but unless I'm misunderstanding the graph, it doesn't appear(to me) to be significant (or at least at the same proportion as cue weight increases). For example, the graph seems to illustrate that for an 11 oz different in cue weights (14-25), there is only around a 18%-19% overall difference in cue ball speed (as a percentage of stick speed). So if you have a 14 oz cue, the cue ball is travelling 1.21X faster than the stick. For an 18 oz cue, 1.31X faster and for a 25 oz cue, about 1.39X faster.
This 18-19% difference in overall velocity is less than the actual increase in stick weights (25oz cue 178% heavier than a 14oz cue). This comparison is probably not an analogous one. But if you look at it from the angle of velocity difference between common cues at a pool hall (say between 17oz and 22 oz), there is only around 7% difference in cue ball speed (~129% for the 17 oz cue vs ~136% for the 22 oz cue) when cue weight increases by 29% (increasing cue from 17oz to 22oz (5oz) is around 29% increase in mass).
I think this understanding is confirmed in the commentary under the graph that says "Notice that for a given cue speed, more cue weight gives more cue ball speed, as one would expect. Although, the benefit of the added weight diminishes at at [sic] higher weights."
And, looking at the graph on p. 10, although the overall cue ball speed percentages are higher, it appears that the slope of the line representing the change in percentages is about the same.
My reading is that for every ounce heavier you go, you get around a 1.4% [relative] increase in cue ball speed.
I'm not smart at the maths, but I stayed at a Holiday Inn once, so there is a 10% chance I'm reading those graphs right.
-td