Thought I might add some extra comments to those very good and comprehensive examples of the aero v weight scenarios that Robert provided last year.
In particular the dynamic scenario of accelerations on flat terrain, which is a little more complex than steady state cycling.
Some might think light wheels would accelerate better than heavier aero wheels, but it's not necessarily the case. Indeed it's more likely the opposite is true, since once you are travelling at speed, the energy demand is dominated by two factors; changes in kinetic energy (including rotational) and overcoming substantial and ever increasing air drag.
If you reduce the energy demand for overcoming air drag, then the energy required for that can instead be used to increase kinetic energy.
Whether or not that results in a performance gain comes down to the starting speed, how long the acceleration lasts for, as well as the magnitude of the aerodynamic and mass differences.
I go through this issue in some detail in this blog post I did last year:
In that item I compare 10-second long accelerations from zero speed and from a starting speed of 30km/h. In the examples I used a typical aerodynamic difference I have measured between such wheels, and an exaggerated difference in wheel mass of 0.5 kg.
Results are plotted on charts.
Turns out that if you are starting the sprint rolling from speed (in this case 30km/h), the heavier aero wheel rider edges ahead immediately and their lead continues to grow. The heavier aero wheel is always the better choice in that scenario (notwithstanding the myriad of other wheel choice factors - which I outline the in the linked post):
However it's a little different from a dead stop where the lighter wheel rider has an initial advantage, however the heavier aero wheel rider begins to catch up and over takes the lighter wheel rider after about 7 seconds, and thereafter rides away from the lighter wheel rider.
So a hot dog crit with the near dead stop turns presents an interesting dilemma, and perhaps could benefit from more individualised assessment. Else if the racing never really slows down all that much for corners, then an aero wheelset is almost always going to be faster and/or require less energy, and accelerate faster.
Of course the exact scenario for any individual depends on the shape of their sprint power vs time plot as some riders have a higher peak power, some riders experience a more rapid power fades, and so on.
The principles however don't change, as the nature and overall shape of the plots will be similar since the energy supply is fixed and it goes to overcoming the total of each energy demand factor, i.e kinetic energy changes, overcoming air drag, rolling resistance, potential energy changes (gravity), drivetrain friction. Require less energy for one, and more is available for the others.
In that item I also cover the impact of differences in rotational wheel mass / moment of inertia, which turns out to be such a small factor it's almost negligible.