Xprize and tethered space station

I read an article about a theoretical tethered space station, where a
long cable was payed out from the surface and attached to a space
station, there are obvious technical problems to overcome but
notwithstanding them it makes sense in a logical way to attach an
object with a wire to a spinning object but would you be weightless in
this type of station.
Now a stationary object in space must travel at 25000 mph (roughly) to
stay orbital but a cable extending upward from the surface would be
stationary and subject only to local winds. where does the transition
occur?
There seems to be gap in my knowledge about how gravity works.

What I understand about Scaled and others Xprize contestants is that
they are suborbital, that is, they are lobbing a craft vertically
upwards as far as they can afford and then falling back to earth when
gravity reaffirmes it's grip.

Not to take anything away from this endeavor but it seems to me a long
way from full orbital flight.

When the X planes of the late 50's flew they came very near space and
orbital flight and if research had continued maybe they could have
acquired the extra boost to go orbital but they had the same problem
the Shuttle has, that is disipating the heat (energy) of slowing down
when they decide to come home.

I am not technically trained but have been an interested observor for
the past 40 years and I would appreciate an explanation of the
dynamics (physics) of the next step that will send the Xprize
contestants into full orbital flight.