Weighted Walking Stick ruling needed

Just want to be sure
Say vampire have WWS with one counter. Does it mean that he cant play another copy of WWS on top, replacing the first one?

Weighted Walking Stick

Only usable before range is determined during the first round of combat.
Put this card with 5 counters on it on this minion; it becomes a melee weapon equipment that can strike: strength+1 damage. For each damage inflicted by this strike (even if prevented), burn 1 counter from this card. Burn this card if it has no counters. A minion can have only one Weighted Walking Stick.

Correct, it can’t play another WWS because of the card text of the WWS in play preventing it....”A minion can have only one Weighted Walking Stick.”...furthermore there is no replacement effect to talk about, it doesn’t have that effect/work like that.

That is what I thought, thanks!