A strong edge-coloring of a graph G=(V,E) is a partition of its edge set E into induced matchings. The edge weight of a graph G is defined to be max{dG(u)+dG(v)|e=uv∈E(G)}. We study graphs with edge weight at most 7. We show that 1) every graph with edge weight at most 6 has a strong edge-coloring using at most 10 colors; and 2) every graph with edge weight at most 7 has a strong edge-coloring using at most 15 colors.