NewSize = 7;
landareas = shaperead('landareas.shp','UseGeoCoords',true);
ax = axesm ('miller', 'Frame', 'on', 'Grid', 'on');
geoshow(landareas,'FaceColor',[1 1 .5],'EdgeColor',[.6 .6 .6]);
set( findobj(ax.Children, 'Tag', 'MLabel'), 'FontSize', NewSize)
Note that this will probably end up shifting the positions of the labels. With the default meridian labels at the top of the graph, the text is generated with VerticalAlignment 'bottom', but with positions just outside the axes. Effectively the text position has been set to have its bottom at the top of the box. If you wanted the text to move further away from the top of the axes box, then the Position properties would need to be changed.