Personally I believe the eyes thing came into play most with book 6 where it was Harry's / Lily's eyes staring at the-new-professor-whos-name-I-can't-remember that made him give up the memory of the Horocrux w/ dear old Voldi.
Plus I think it did serve as a constant reminder to Snape that James won Lily. That James fathered Harry. That no matter how much Snape loved Lily, she was never his. And that no matter how much he desperatly wishes that Harry looked like him and had Lily's eyes, he knows it can't ever be.
Harry is a walking reminder of Snape's deep Love/Hate thing regarding the Potters and that night etc. Lily/James.
I also think the eye thing is just another reminder of his mothers love and his parents and as a character development piece. It's his description : You look just like your father, except for the eyes. You have Lily's eyes.
It's an easy way to consistantly describe Harry without describing him TOO much. Brilliant on JKR's part. LOVE her.
"If you can talk, you can sing...if you can walk, you can dance."
- T.K. Greene