Weaken resolve states "The Dark Angels Librarian forces his way into the minds of his foes, robbing them of their will to fight and eroding whatever resistance they possess."

From Beyond states "The mind of a creature with this trait is beyond the petty frailties and precarious sanity of a mortal mind. It is immune to Fear, Pinning, Insanity Points, and psychic powers used to cloud, control, or delude its mind."

Weaken resolve definitely does not control the mind, but depending on how you read it, it may work through clouding or deluding the mind. From Beyond does not provide immunity to psychic powers in general, though, or stat reductions from them, or even psychic powers that affect the mind or weaken it (merely ones that cloud, control, or delude it), so an argument could be made that it would not protect against it. I'm thinking that the intention of the trait would be to protect against that effect, but am wondering as to what other's opinions might be.

Personally I would say that Weaken Resolve wouldn't work on a creature with the 'From Beyond' trait for the reasons you have given in your counter argument (i.e Weaken Resolve works to cloud control and delude).

Further most From Beyond creatures are such that they don't have resolve, will or indeed a mind that could be readily understood and exploited by a human psyker. I am primarily talking about daemons here but I am sure certain particularly horrific and bizzare aliens would also come into this category.

No, it does not affect creatures with From Beyond.

The power is undoubtedly a mind affecting power and From Beyond undoubtedly provides protection from mind affecting powers.