Looks like you will need a sensor with more accuracy and resolution, which is possible with calibration and a frontend circuit…
But the weight method is not recommended, as there is no way to detect duplicate coins of same weight. But for academic project, it should be ok.
To get his working, You need to get a load cell with driver (These will come with display for weight).
If you go to nearest weighing machine repair shop, they can calibrate and give it to you for getting smaller weights measured with good accuracy. And also check if you can get driver boards with RS232 interface, which you can easily interface with MCU.
I had done a Automatic groceries dispenser in this way, But i tapped the driver output lines to MCU ADC pin and measured from there.