What is the effect of rotational frame dragging on an object constrained in equatorial non-free falling trajectory?

The wikipedia article about frame dragging mentions the following fact about rotational frame dragging:

Another interesting consequence is that, for an object constrained in an equatorial orbit, but not in freefall, it weighs more if orbiting anti-spinward, and less if orbiting spinward. For example, in a suspended equatorial bowling alley, a bowling ball rolled anti-spinward would weigh more than the same ball rolled in a spinward direction. Note, frame dragging will neither accelerate nor slow down the bowling ball in either direction. It is not a "viscosity".

I would like to ask which one of the following situations is being described here, because the wording above is unclear:

1) The bowling ball weighs more in the sense that, if we imagine the suspended bowling alley covered with sensors, they register the ball to be heavier in anti-spinward (and lighter in the spinward) direction, compared to the case of an alley suspended above a non-rotating massive body.

2) The bowling ball weighs more in the sense that one requires more force to roll it in the antispinward direction (and less to roll it in the spinward direction) compared to the case of an alley suspended above a non-rotating massive body.

Of course, regardless of which one of the above interpretations is correct, I would expect that the same is valid also for an object of generic shape, even if the constraining surface is drag free.

The first case sounds analogous to what happens inside a rotating space station. Both of the above interpretations looks plausible to me.

I would also like to see the math justifying whichever interpretation is the correct one, since wikipedia doesn't provide any.