In the subcategory of topological vector locally convex spaces Hausdorff are built proper classes of weakly reflective and weakly coreflective subcategories, respectively. We proved that the right product of two subcategories often leads to a weakly reflective subcategory, which is not reflective. A full subcategory R of category C is called weakly reflective, if for any X 2 jCj there are an object rX 2 jRj and a morphism rX : X ! rX with the property: for an object A 2 jRj any morphism f : X ! A extends through rX : f = g ¢ rX for some g. If the extension is always unique, then R is called the reflective subcategory. In universal algebra, reflective subcategories are realized as factorizations of objects, but extensions are also known, for example localizations in torsion theories. In the general topology, reflective subcategories are more common as extensions, but there are also some as factorizations. In the subcategory of topological vector locally convex spaces Hausdorff C2V are known proper classes of reflective, coreflective and bireflective subcategories. In C2V we construct weakly reflective subcategories and weakly coreflective subcategories and study their properties. We denote by R (respectively K ) the class of non-zero subcategories of category C2V. For K 2 K and R 2 R with the respective functors k : C2V ! K and r : C2V ! R, either ¹K = fm 2Monojk(m) 2 Isog, "R = fe 2 Epijr(e) 2 Isog. Both ¹K and "R are classes of bimorphisms. If B is a class of bimorphisms and A a subcategory, then SB(A) (respectively QB(A)) is the full subcategory of all B-subobjects (respectively: Bfactorobjects) of the objects of subcategory A. We examine the following two conditions: a) R contains the subcategory S of spaces with weak topology; b) K contains the subcategory ~Mof spaces with Mackey topology. Theorem 1. Let be rX = uX ¢ vX is the ((¹K)>; ¹K)-factorization of morphism rX, kX = wX ¢ tX is the (("R); "R?)-factorization of morphism kX. 1. S¹K(R) is a weak reflective subcategory of the category C2V and vX : X ! vX is the weak replique of object X. 1¤. Q"R(K) is a weak coreflective subcategory of the category C2V and wX : wX ! X is the weak coreplique of object X. 2. S¹K(R) is a reflective subcategory if it meets one of the conditions a) or b). 2¤. Q"R(K) is a coreflective subcategory if it meets one of conditions a) or b). Theorem 2. Let R 2 R and let § be the coreflective subcategory of the spaces with the most powerful locally convex topology and ¾ : C2V ! §. The following statements are equivalent: 1. S¹§(R) is a reflective subcategory of the category C2V. 2. S ½ R. Theorem 3. Let K 2 K and let ¦ be the reflective subcategory of the complete spaces with weak topology and ¼ : C2V ! ¦. The following statements are equivalent: 1. Q"¦(K) is a coreflective subcategory of the category C2V. 2. ~M ½ K.