Confluent with the single dimension of time, breach of time-reversal symmetry is usually perceived as a one-dimensional concept. In its ultimate realization - the one-way guiding device - it allows optical propagation in one direction, say +z, and forbids it in the opposite direction -z. Hence, in studies of time-reversal asymmetry the mapping t-t is naturally associated with z-z. However, strongly nonreciprocal or one-way nanoscale threads can be used to weave metasurfaces thus adding dimensions to this concept. In this new family of surfaces the aforementioned association cannot be made. An example of appropriate threads is the planar one-way particle chains based on the two-type rotation principle. The resulting surfaces - the metaweaves - possess generalized nonreciprocity such as sector-way propagation, and offer new possibilities for controlling light in thin surfaces. We study several metaweave designs and their asymmetries in the wave-vector space.