Wilia was told by her father that this sword had been passed down from generation to generation. If a Walheimstein was worthy, the sword would be passed down to him.
Wilia just realized that what is meant by being worthy does not mean that she is strong, because she has admitted her defeat and weakness during the fight against Nina. Apparently, the sword was given when Walheimstein was an adult.
According to Leashira's explanation, this sword allows anyone to use it regardless of age or how strong the user is. The sword only asked for one thing, which is fresh blood.
Not just any blood, but specifically the blood of the Walheimstein family which was supposedly a direct descendant of Euka. Because if someone outside the Walheimstein family uses it, the sword will resist and instead give poison that is stabbed through its thorns into the person's body and will end up dead.
"Okay, so how are you feeling right now?"