Regarding the hesitation problem when playing large rolls on your
Weaver, Standard action player there are two things you might want
to check, either one of which could be contributing to your problem:
the upper and lower transmission brakes and the spring tension on
your idler pulley. What you call a "pressure pad" is usually referred
to as a brake and their are two of them on a player transmission, the
upper brake, which engages when the transmission is in "play" and the
lower brake, which comes into play when the transmission is in "reroll".
One or the other of these is always engaged, but the two are never active
at the same time. The purpose of the upper brake is to put just enough
tension on the roll during "play" that it passes over the tracker bar
without "fluttering". Too much tension here will impede tracking because
excessive friction will hinder the roll from moving from side to side.
The purpose of the lower brake is to put sufficient tension on the roll
during "rewind" to ensure that the roll rewinds back onto it's original
spool tightly enough so that there is no slack , so the problem you
describe--that of hesitating during "play" won't happen the next time the
roll is played. Your problem therefor may lie not with the upper brake, but
with the lower one. Testing the lower brake is easy, you don't even need a
roll to do so. Simply put your transmission into "reroll" and try spinning
the take-up spool by hand. Does it spin freely?  Well, it shouldn't! Try
increasing the tension on the lower brake and see if your rolls don't
rewind more tightly. This could solve your problem. You see when you
momentarily stop the roll from turning with your hand, you're not only
taking up the slack in the take up spool, but in the roll itself. If
increasing the braking action of the lower brake doesn't completely fix
your problem, look at the chain connecting the air motor gear with the
transmission. The purpose of the idler pulley is to maintain sufficient
tension on the chain so the there is no slack. It could be that the idler
pulley spring is too weak. As the large roll is being played, more and
more of it accumulates on the take-up spool, increasing the effort
necessary to turn the roll. If you're not maintaining sufficient tension
on the chain, you may actually see it hesitate as slack appears as the
roll nears it's end. Either increasing the tension on the lower brake,
or increasing the tension of the idler pulley should correct your problem.
Why do some large rolls cause a problem and others don't. Because some
large rolls, especially the older ones were printed on heavier paper than
the newer ones and the heavier the roll, the more pronounced the problem
will be. Sorry that this response is so long, but I hope you find it to
be of some help.

Les Smith