"Is it a grave matter to eat meat, knowingly and without necessity, on a Friday in Lent?"

This is more related to moral theology than liturgy. There are sins in which the matter may be grave or not grave according to other circumstances. For example, stealing even a small sum would be grave matter if the thief knows the victim to be desperately poor and needy. It would not necessarily be grave matter, although still a sin, if it represented a slight loss.

Considering this, I would say that the act of eating meat on a Friday of Lent could be grave or venial according to other circumstances. If this act is carried out knowingly, without necessity in such a way that the Church's laws are openly despised and denigrated, then it would be grave matter and should be confessed as such.