If you want different colours but the same thickness then you can set the thickness with BaseStyle
ParametricPlot3D[{{t, 0, -t}, {0, t, 2 t}}, {t, 0, 100},
BaseStyle -> AbsoluteThickness[5], PlotStyle -> {Blue, Orange}]
...otherwise
ParametricPlot3D[{{t, 0, -t}, {0, t, 2 t}}, {t, 0, 100},
PlotStyle -> {{Blue, AbsoluteThickness[15]}, {Orange,
AbsoluteThickness[5]}}]
or (probably better)
ParametricPlot3D[{{t, 0, -t}, {0, t, 2 t}}, {t, 0, 100},
PlotStyle -> {Directive[Blue, AbsoluteThickness[15]], Directive[Orange,
AbsoluteThickness[5]]}]
BTW, what is happening when you have PlotStyle -> {Blue, Orange, Thickness[100]}
is that your first bunch of data is styled blue, your second bunch of data is styled orange and your third bunch of data is styled "mega-thick" ...but you don't have a third bunch of data. So if you try this instead
ParametricPlot3D[{{t, 0, -t}, {0, t, 2 t}}, {t, 0, 100},
PlotStyle -> {Blue, Thickness[1], Orange}]
now the second lot of data is styled thick. etc.