Answer
$615N$
Work Step by Step
We know that
$F=PA$
$\implies F=(70.51\frac{lb}{in^2})(1.01\times 10^5Pa)(14.7\frac{lb}{in^2})(2\times 7.13cm^2)(\frac{1m}{100cm})^2$
$F=690.7N$
The net force is given as
$F=W_{my\space weight }+W_{bicycle}$
This can be rearranged as:
$W_{my\space weight}=F-m_{bicycle}g$
We plug in the known values to obtain:
$W_{my\space weight}=690.7-7.7(9.8)$
$W_{my\space weight}=615N$