If brane theory says that gravity is weak because it extends into another spatial dimension, is it also saying that the gravity attributed to dark matter might be due to matter in another spatial dimension?
string theory does offer possible candidates for dark matter since since many theories include a LOT more particles and forces than has been observed (detected). String theory seems to offer no specific predictions as to which of many possible candidates are the dark energy or dark matter
Just to be careful, branes are not 2D strings. Branes are nonperturbative objects that arise as solutions to the supergravity equations of motion. They can be in any number of dimensions (up to the total dimensionality of the theory), although some string theories can only have odd or even dimension branes. The proper notation is a Dp-brane, where p denotes the number of spatial dimensions. Most popular brane world models posit our universe to be a D3-brane, with 3 uncompactified spatial dimensions.None that I have read about. There are a LOT of string theories out, many have branes; that is two dimensional strings.