Consider a planet in some solar system which has a mass double the mass of the earth and density equal to the average density of the earth. An object weighing W on the earth will weigh : 

2^1/3W

Since the density is same the volume and hence the radius of the planet will be more than the radius of the earth. Let the radius of the earth be R and that of the planet be R'.

If the density is ρ, then  4πR'³ρ/3 = 2*4πR³ρ/3 

\(\Rightarrow\) R'³ =2R³  

\(\Rightarrow\) R' = 2¹/³R 

Acceleration due to gravity on this planet = G x 2M/R'² (M is mass of the earth) 

  =2GM/(2¹/³R)² 

  =2⁽¹⁻²/³⁾(GM/R²) 

  =2¹/³g 

Hence the weight on the planet =2¹/³*mg =2¹/³W