Is gravity the killer of dimensions?

Here's a hypothetical. If Superstring theory is right and there are
extra dimensions beyond the 3 space and 1 time dimension, and that those
extra dimensions are just rolled up into loops that are probably the
size range of the Planck Length, then is it possible that reason we
can't access those extra dimensions is because we're stuck by an
extra-dimensional and superstrong form of gravity to the surface of a
3-dimensional membrane?

Let's pull back a little and look at life on our existing 3-D universe.
Although we're supposedly 3-dimensional objects, we mostly just have
freedom of movement in only 2 dimensions while on the Earth, because
we're stuck to the surface by gravity. We can access the 3rd dimension
(height) but only by expending some large-ish amount of energy. If we
were out in space, and unhindered by gravity, we'd have freedom of
movement in all 3 dimensions. Now if we're not on Earth and instead on
some kind of Super-Earth where we weigh more, then we'd have to expend
even more energy to access the 3rd dimension. Now let's get even more
extreme: if we were on the surface of a white dwarf or a neutron star,
then we'd have been crushed down and splattered across its surface into
a stain no more than one or two atoms thick! So to access the 3rd
dimension would require even more energy, almost an impossible amount of
energy, and for all intents and purposes, we'd be 2-dimensional objects
on this surface.

Then let's get even more extreme, how about if we're approaching a black
hole? Here there's no surface to land on and get splattered on, like
with the white dwarf or neutron star. Instead as we approach the event
horizon, we first get spaghettified into a one-dimensional stream of
atoms. Then after we've passed through the event horizon, we approach
the center, and we get crushed into a zero-dimensional singularity. So
the progression is obvious here, the stronger the gravity, the less
dimensions there are.

I'm wondering if it also goes the opposite way? Let's say as gravity
becomes less and less stronger, that more than 3 dimensions start to
open up to us? And I'm wondering if the strange behavior that we have
attributed to Dark Matter and Dark Energy are just the behaviour of
extra dimensions opening up?

Yousuf Khan