Aspire one ZG5 CCHANGES THE ZOOM LEVEL ON ITS OWN

Go to Control Panel > Mouse > Device Settings > Settings > Advanced Gestures > Pinch

(or alternatively right-click the Synaptics Pointing Device icon in your taskbar and select Pointing Device Properties)

Untick the box that says 'Enable Pinch'. This will disable the zooming.

Additionally, you might be suffering the same problem as I was which was I had no idea how to use the zoom and that's why I wanted to lock it. Once I learned, I've decided the zoom is useful and I'm keeping the feature enabled.

Here is what Synaptics have to say about the 'pinch' gesture:
The Pinch gesture delivers zooming functionality in many applications. The Pinch gesture can be used to perform the same function as a scroll wheel on standard Windows applications that support CTRL-SCROLL WHEEL zoom functionality.

To perform a pinch gesture, place two fingers on the TouchPad surface. Move them closer together or further apart. To zoom in, place your fingers on the TouchPad surface near to each other and then slide them apart. To zoom out, begin by placing your fingers apart and then moving them closer together.

The best zooming experience results when the finger tips of the two fingers are used for the gesture.

That will hopefully be of assistance if you want to learn how to use the zoom rather than disable it.