You're looking at two different kinds of verbs, each with it's own behavior.
The book sells.
The door opens.
These verbs are ergative. When transitive, their subjects represent semantic actors or agents, and their objects represent semantic patients. When intransitive, the subjects represent patients.
Ergative clauses carry semantics similar to reflexive or passive clauses:
Ergative ---> Reflexive / Pasive
The book sells. ---> The book sells itself. / The book is sold.
The door opens. ---> The door opens itself. / The door is opened.
The pencil writes.
Some students bully.
These verbs are not ergative. The absence of an object here does not make these subjects into patients.
Non-ergative clauses have different semantics than reflexive or passive clauses:
Non-Ergative -X-> Reflexive / Pasive
The pencil writes. -X-> The pencil writes itself. / The pencil is written.
Some students bully. -X-> Some students bully themselves. / Some students are bullied.
An ergative clause neither requires nor allows an agent.  meant;
The book sells by that shop. -X-> That shop sells the book.
The door opens by John. -X-> John opens the door.
Even if "bully" were ergative, your example sentence would still contain an error. You'd have a verb that claims to have no agent combined with a prepositional phrase that claims to be the verb's agent. What agent (except Schrodinger's cat) can both exist and not exist in the same container at the same moment?
The sentence that you want is:
Weak students are easily bullied.
The passive voice implies that an agent exists, but does not require that that agent be supplied.
I mean the plain arrow ( ---> ) to represent "is similar to" and the crossed-out arrow (-X-> ) to represent "is not similar to". Clauses after the crossed-out arrow are not necessarily wrong. They're simply not related to the clauses before the arrows.