Weave has other issues... like they homebrewed their own ECDHE-PSK-based transport encryption protocol on top of NaCl. Homebrewing your own crypto, especially transport encryption which has to solve problems like key exchange, replay attacks, etc is generally the wrong answer.
Also, even if they were using a standard transport encryption like SSL/TLS or IPSEC, PSKs are generally frowned upon for anything other than point-to-point connections.
They describe the PSK as a "password", so what they really want is a PAKE algorithm, however they do not use a password hashing function, so weak "passwords" are susceptible to brute force attacks.
Anyway, all these things are why you should just stick to standard protocols like SSL/TLS or IPSEC.
Also, even if they were using a standard transport encryption like SSL/TLS or IPSEC, PSKs are generally frowned upon for anything other than point-to-point connections.
They describe the PSK as a "password", so what they really want is a PAKE algorithm, however they do not use a password hashing function, so weak "passwords" are susceptible to brute force attacks.
Anyway, all these things are why you should just stick to standard protocols like SSL/TLS or IPSEC.