Referring to the  diagram  I have posted  below .

In  the  shaded region labeled  'A',  I think there could be either :

   ( 1 ) - A magnetic mechanism  that swings( or releases ) the  weight down( in the direction of rotation )  'BEFORE'  it would normally be swung/released down if it just relied on gravity

   ( 2 ) -  A mechanical mechanism that that does the same as ( 1 )

   ( 3 ) -  A spring ( or, a spring latch ) mechanism  that that does the same as ( 1 )

   ( 4 ) -  OR,  a combination of any of the above
 
OR,  In  the  shaded region labeled  'B', a  mechanism  could  be raising/returning the weight back to it's position close to the rim of the wheel,  BEFORE that would normally happen if just relying on gravity .

    The mechanism/mechanisms would be  activated by  it's  angle to gravity,  to cause things to happen  earlier ( or later ) than they normally would by just relying on gravity ).

POSSIBILITY 1
This mechanism could exist either on the wheel itself,  or,  on a static structure next to the wheel .
(  Could it be that the  force from one  weight falling at  9:00-O'clock  then  re-lifts  a weight at  between  9:00-O'clock  and  6:00-O'clock ,   or pushes a weight( between 9:00-O'clock and 12:00-O'clock )   to fall early  .   Could that  mechanism  be  magnetic  or  cog-wheels ,  to transfer the force collected from a falling weight to help  budge  another weight  to fall early,  or to be  re-lifted  early   )

POSSIBILITY 2
Each weight has it's own individual  mechanism (  activated by  it's  angle to gravity,  to cause things to happen  earlier ( or later ) than they normally would by just relying on gravity ).