  2T-gravity in d+2 dimensions predicts 1T General Relativity (GR) in d
dimensions, augmented with a local scale symmetry known as the Weyl symmetry in
1T field theory. The emerging GR comes with a number of constraints,
particularly on scalar fields and their interactions in 1T field theory. These
constraints, detailed in this paper, are footprints of 2T-gravity and could be
a basis for testing 2T-physics. Some of the conceptually interesting
consequences of the "accidental" Weyl symmetry include that the gravitational
constant emerges from vacuum values of the dilaton and other Higgs-type scalars
and that it changes after every cosmic phase transition (inflation, grand
unification, electroweak phase transition, etc.). We show that this
consequential Weyl symmetry in d dimensions originates from coordinate
reparametrization, not from scale transformations, in the d+2 spacetime of
2T-gravity. To recognize this structure we develop in detail the geometrical
structures, curvatures, symmetries, etc. of the d+2 spacetime which is
restricted by a homothety condition derived from the action of 2T-gravity.
Observers that live in d dimensions perceive GR and all degrees of freedom as
shadows of their counterparts in d+2 dimensions. Kaluza-Klein (KK) type modes
are removed by gauge symmetries and constraints that follow from the 2T-gravity
action. However some analogs to KK modes, which we call "prolongations" of the
shadows into the higher dimensions, remain but they are completely determined,
up to gauge freedom, by the shadows in d dimensions.
