Hi Flossy P,
A single Point wont scale, as only the X, Y, Z coordinates are stored.
IF you scale from a different position (Based on the axis for the selection), then all what will happen is movement. This is typically the case for a group of points.
The Size of points in the GUI [graphical user interface] can be changed. Editor View>>Options>Configure…/Configure All …>>Attribute manager>View>Point Handle Size
What is your target, if none of the above fits to the question?
All the best
