I am not certain what you want.
Try this:
errs = rand(1,10);
x = 1:10;
y = randi([10 20],1,10);
figure
plot(x, y)
hold on
heb = errorbar(x, y, errs, '.');
hold off
grid
heb.LineWidth = 2;
The error bars and the caps are both linewidth=2 here, with everything else being the default properties.
