I read in the book INTRODUCTION TO ROCKET SCIENCE AND ENGINEERING by T.S.T that Rocket Engineers design how big the throat of the nozzle should be based on the Weight Flow Rate. So my question is HOW?
I assume you are referring to page 97 of the Taylor book
The thermodynamic properties of the engine (combustion, gas dynamics, and nozzle design) will determine the I sp . The overall weight of the spacecraft and rocket combination will drive the thrust requirement. And, having these two values allows us, through Equation 3.18, to determine the weight flow rate of propellant mass needed, which will lead to design knowledge about how big the nozzle throat of the rocket must be.
You can refer to his equation 4.50 on page 143 to calculate throat area (although it's mass flowrate you use, not weight flowrate).
For a version with less tortured syntax, you can check out the online version of Sutton, page 61, which gives a worked-out example.