One could posit that the negative security impact on such a password is negligible, since the password is already weak. I think it would be worrisome if there

One could posit that the negative security impact on such a password is negligible, since the password is already weak. I think it would be worrisome if there weren't protective measures already in place, such as limited login attempts, two-factor auth, and so on. The other weakness would be the repetition of that password on sites that place a low priority on, or are ignorant about, security. At which point, it doesn't even matter.