It is surely impossible not to feel some sympathy for Eugene. He was what Massive Dynamic, uncaring scientists treating him like an animal and the world had made him. I didn't feel he was stalking Julie (the woman in the elevator) so much as he had no clue how to interact with her at a normal level. He clearly had no evil intent against her. The moment her reaction to his gift was fear he immediately left the apartment.
I don't feel entire sympathy for him though because he was, let's face it, killing perfectly innocent strangers in order to fix himself. So he loses a whole lot of Brownie points there.