Minimum number of below average triangles in a weighted complete graph

Let GG be an edge weighted graph with nn nodes, and let A(3,G)A(3,G) be the average weight of a triangle in GG. We show that the number of triangles with weight at most equal to A(3,G)A(3,G) is at least (n−2)(n−2) and that this bound is sharp for all n≥7n≥7. Extensions of this result to cliques of cardinality k>3k>3 are also discussed.