\version "2.12.0"

\header {

  texidoc = "The thickness setting between markup lines and other
  lines is consistent."

}

\new Staff {
  \override TextSpanner #'bound-details #'right #'text =
        #(markup #:draw-line '(0 . -1))
  \override TextSpanner #'thickness = #2
  c'4 \startTextSpan
  c'4 \stopTextSpan
}