I think Beth was constantly overlooked by the family and shoved into some dark corner. Perhaps it interfered with her psyche. She was absolutely gaga over Peter. But in my opinion she was a crazed lunatic. Not my most favorite episode either. She deserved what she got in the end.
The entire plot was centered around her mental stability. So many families have the "odd" one and do their best to keep him/her safe within the confines of family life. Unfortunately Beth had delusions of grandeur, evidenced by the dreamy death scene which quickly unravelled in real life. Sorry - of all the murderers she desperately needed locking up!