Line Thickness Again: linethickness

\setlength{\unitlength}{1cm}
\begin{picture}(6, 8)
  \multiput(0, 0)(6, 0){2}{\line(0, 1){8}}
  \multiput(0, 0)(0, 8){2}{\line(1, 0){6}}
  \linethickness{.075mm}
  \put(0.5, 3){\line(1, 0){2}}
  \put(3, 2){\line(2, 1){2}}
  \put(5.5, 0.5){\line(0, 1){3}}
  \put(1, 1){\circle{1.3}}
  \qbezier(1, 0.1)(4.5, 1)(2, 2.5)
  \put(4.3, 1.3){\oval(1.6, 1.9)}
  \linethickness{1mm}
  \put(0.5, 7){\line(1, 0){2}}
  \put(3, 6){\line(2, 1){2}}
  \put(5.5, 4.5){\line(0, 1){3}}
  \put(1, 5){\circle{1.3}}
  \qbezier(1, 4.1)(4.5, 5)(2, 6.5)
  \put(4.3, 5.3){\oval(1.6, 1.9)}
\end{picture}