Could it be possible to show the component layer of the same master as the layer clicked?
For example, if I have a tab with the tcedilla layer set to “Thin,” but the master selected is “Bold,” when I double-click on my t component, it shows t - Bold. However, it would be more logical to show t - Light no ?
Fair enough. It’s a bit more tricky though. In your example, your layers are the same as the masters (which makes me wanna ask: why do you pick the layers in the sidebar and not switch with the master switcher?). But it can be more complicated. A brace layer where you don’t have the exact same base glyph, and the associated master may not be even close. Or a bracket layer or backup layer, where there is at least an associated master.
I’m using a lot of QA scripts that open a new tab with problematic layers.
These tabs contain layers from different masters.
Special layers are always associated with a master, even if it’s not the closest to the brace coordinates. In this case, I agree it could show the wrong layer, but this is because designers incorrectly associated the special layer with the master.
Could something be done about this? It really makes my work painful since I always have to select the correct master after clicking on a layer.
I think it might not bother most users, but as a font engineer, I use Font.newTab() a lot to work with layers from different masters. 
Through scripting it’s easy. Use newTab() with a list of GSLayer objects.
That’s already what I’m doing…
Try this: click on an “A” component, and you will see that it shows the layer of the selected master, not the component layer.
Font.newTab([layer for layer in Font.glyphs["Acircumflex"].layers])
I’ll have a look.
Any news about this @GeorgSeifert ? 
Could it be possible to display the component with the same master as the clicked glyph when double-clicking on it?
It would make me really super happy
Me too!