Wouldn't using nuclear weapons in Ukraine be a sign of weakness?

It is. But if the world does not respond with full destruction of Russia, it might be viewed as clever way to win a war and provoke even greater horror.

It is important to make this point very clear to Russia right now that such action will be not tolerated and it will provoke full nuclear response.

Otherwise when they think that there will be no response out of fear, they might consider its possibility.

I do not rule out thy using a single small nuclear weapon against a mostly military target would get unanswered. If so, I think it could be seen as a sign of strength “look what I can get away with”.

Also, even if it is a sign of weakness, if the alternative would be not winning the war, which one would be the lesser evil, seen from the viewpoint of prestige?

You might interpret it as a sign of weakness. Some people seem to interpret using ridiculously overpowered weaponry as a sign of strength or virility.

It ain’t trickin’ if you got it.