Leftyretro First your going to have to learn more about pressure sensors. Don't worry, it's not difficult to understand and can be quite educational.
The sensor you have selected is in fact a differential pressure sensor. That means it measures the relative difference between it's two pressure ports (P1 & P2). Some of these sensors only give you physical access to one port but the second port is still there internally and is sensing the ambient pressure. Because the sensor can only respond to a differential pressure between it's two ports, it will never be able to sense a change in barometric pressure changes. As barometric pressure changes both ports will sense the same amount of pressure and therefore have a net zero differential pressure between them and a measurement "zero output".
What you need is called an absolute pressure sensor. While internally it still has two pressure ports, one port has had a vacuum pulled on it and then sealed tight. Therefore the second port will always be sensing the pressure difference between it's port and the fixed 'reference' pressure and is suitable to measure barometric pressure changes (as well as vacuum pressure values)if sensitive enough.
Another area to understand with these kind of pressure sensors is that they come in generally two styles. First kind is what you might call a raw sensor. It is basically just a resistive Wheatstone bridge circuit where you supply a fixed driving voltage or current and you measure the voltage differential across the bridge (usually in millivolt range) to sense the pressure differential. The second kind of sensor has more electronics integrated in the sensor and amplifies the voltage to a more useful range and often has temperature compensation built in to make for a more reliable and accurate sensor. Of course the second kind costs a little more but can help make for a more successful result. The sensor you linked to is an example of a sensor that has built in amplification and compensation.
So to recap you need to understand and specify the type of pressure element you need, differential or absolute. Then you need to determine the range of pressure measurement the sensor is designed to measure. And finally you need to determine if you want a raw sensor or one with built in amplification and compensation.
I've built several barometric pressure gages over the years and had a lot of fun learning about that field. Did you know that a well calibrated and sensitive barometric pressure can be used to measure elevation?
Good luck
Lefty
PS, You don't need to be a weather man to know which way the wind blows........