You need to get a handle to the scattergroup object to change the marker properties. As proposed by Jonas in a comment, you can get it easily by
% get handle to scattergroup object
h = gco;
Since the scatter group is a child of the axis, you could also get it by
% get handle to scattergroup object
h = get(gca,'children');
If the image contains more than one graphic object (e.g., additional lines), the command findall
maybe of help (again a suggestion by Jonas). With this command you can search for handles to graphic objects with specific properties:
h = findall(gca,'marker','o')
When you have a handle to the scattergroup, you can change the properties of the marker by
% change size of markers
set(h, 'sizedata', 50)
To see a full list of scattergroup properties that can be changed use
get(h)
or for a GUI that shows the properties use
inspect(h)
If you just want to edit a single plot (i.e. no need for scripting), you can just edit the actual figure by clicking on the mouse button on the toolbar and then clicking on one marker in the plot (again suggested by Jonas). Then you right-click on the marker, select "Properties", then you push the button "More properties". In the UI that opens up you change the entry "sizeData" to a value of your choice.