You could try something like this:
% Code example with slight change (w=)
w=worldmap('World');
load coastlines
plotm(coastlat,coastlon)
% Find grid line objects and modify line width
p=findobj(w,'Tag','Parallel');
m=findobj(w,'Tag','Meridian');
p.LineWidth = 5;
m.LineWidth = 5;
Remove the semicolons or use the property inspector to see what other porperties are accessible for modifying.
