I am looking at how force and gravitational G scale under different unit systems

old_G_value * 1/kg_s * 1/m_s = new_G * (1/kg_s^2)/ (1/m_s)^2
old_G_value * kg_s /m_s^3 = new_G

kg_s =2, m_s =1 so now 1 new kg =2 old kg
old_G_value * 1/kg_s * 1/m_s = new_G * (1/kg_s^2)/ (1/m_s)^2
old_G_value * 1/2 * 1 = new_G * (1*(1/2)^2)/ (1)^2
old_G_value * 1/2 * 1 = new_G * (1/4)/ (1)^2
old_G_value * 1/2 / ((1/4)/ (1)^2) = new_G
old_G_value * 1/2 * (1/(1/4)) = new_G
old_G_value * 1/2 * 4 = new_G
old_G_value * 2 = new_G

kg_s =1, m_s =2 so now 1 new m =2 old m
old_G_value * 1/kg_s * 1/m_s = new_G * (1/kg_s^2)/ (1/m_s)^2
old_G_value * 1/1 * 1/2 = new_G * (1^2)/ (1*(1/2))^2
old_G_value * 1/2 = new_G * 1/ (1/4)
old_G_value * 1/2 = new_G * 4
old_G_value * 1/2 * 1/4 = new_G
old_G_value * 1/8 = new_G