  In the context of six-dimensional conical braneworlds we consider a simple
and explicit model that incorporates long distance modification of gravity and
regularization of codimension-2 singularities. To resolve the conical
singularities we replace the codimension-2 branes with ring-like codimension-1
branes, filling in the interiors with regular caps. The six-dimensional Planck
scale in the cap is assumed to be much greater than the bulk Planck scale,
which gives rise to the effect analogous to brane-induced gravity. Weak gravity
on the regularized brane is studied in the case of a sharp conical bulk. We
show by a linear analysis that gravity at short distances is effectively
described by the four-dimensional Brans-Dicke theory, while the higher
dimensional nature of gravity emerges at long distances. The linear analysis
breaks down at some intermediate scale, below which four-dimensional Einstein
gravity is shown to be recovered thanks to the second-order effects of the
brane bending.
