Newton's law of gravity is given by:
where G is the gravitational constant, m1 and m2 are the masses and r is the distance between them.
To calculate the weight using this law we need to remember that:
![\begin{gathered} G=6.67*10^(-11)(m^3)/(kg\cdot s^2) \\ \text{Mass of the eart:} \\ M=5.972*10^(24)\operatorname{kg} \\ \text{Radius of earth:} \\ r=6.3781*10^6m \end{gathered}]()
Plugging this values and your mass in Newton's law we have:
![\begin{gathered} F=6.67*10^(-11)(m^3)/(kg\cdot s^2)\cdot\frac{(52kg\text{)(}5.972*10^(24)\operatorname{kg})}{(6.3781*10^6m)^2} \\ F=509.17N \end{gathered}]()
Therefore your weight is 509.17 N