The problem of applying Weyl theory for descriptioon of space-time conists of the problem of conection between different points. GR is the simplest theory which is applicable to studies of the space-time as the whole. Weyl theory is aplicable only in the concrete point. That to come to nother point it is necessary built way to another point. in ther words, Weyl theory is local. The local spaces were studied in detail in 1950-60, for example, formalism of tetrades --- 4 local vectors tn every pont. But transfer to another point is difficult with mathematical vtewoiint. GR was xhosen for description of space-time as the simplest one. GR includes field equations which can be solved for different models.