Word to describe someone who fears the strong but bullies the weak
Solution 1:
Pretty sure the best, non-vulgar word for a person like that is already found in your question:
- bully
A few other words you could use that fit the bully aspect:
- Oppressor
- Tyrant
- Despot
A few words that fit your first qualification for the word:
- Craven
- Coward (@John-Wimpey)
- Chicken
Solution 2:
There is a humorous word for this: dastard (not bastard but almost)
A malicious coward; a dishonorable sneak.
http://en.wiktionary.org/wiki/dastard