Boxplots on the variability chart are BoxPlotSeg. This script demonstrates some of the modifications you can make to a BoxPlot Seg. You can cahnge the line width but I do not see a message to change the box width.
Names Default To Here( 1 );
dt = Open(
"$SAMPLE_DATA/Variability Data/2 Factors Crossed.jmp"
);
vc = dt << Variability Chart(
Y( :Measurement ),
X( :Operator, :part# ),
Show Box Plots(1)
);
_xbp = vc <<Xpath("//BoxPlotSeg");
_xbp << set box style("Solid");
_xbp << set box type("Outlier");
_xbp << set fill color ({0,0,221});
_xbp << set transparency(0.3);
_xbp << set line color({0,0,128});
_xbp << set line width(6);