Currently, the dsp.SpectrumAnalyzer by itself does not provide you with the option to change the line width. One of the possible workarounds that you can try is to find all the line objects in your plot and then change their linewidth, like following.
line=findall(0,'type','line'); %finding the line in the figure
line.LineWidth=3; %or whatever you wish it to be
Note that "gca" and "gcf" won't work on this figure unless you turn on the handle visibility property to on (by default it is off).
