In icon sets, variations in stroke thickness is a bad idea, without changing the context. People who can't evaluate design issues would simply categorise the product as "something's off here", or "I don't trust this". Your iconography has an impact at a deeper level.
That doesn't invalidate GP's points. A collection of B&W icons with similar base shapes (circle, square, rectangle) and no contrast is terrible for using the interface. Each icon needs a distinctive element, be it color, weight or shape, to make it stand out from the other icons near it.
If you're designing a B&W icon set, at least make sure that each one has a very eye-catchinge, different outline.
