I think it is possible that he may have wanted to hurt Catelyn for what she had done to him by refusing his love back in Riverrun, seeking some sort of vengeance. The only perspective that we get on their relationship comes from Cat, who claims that he would be glad to see her because of their shared childhood, yet it could be just as likely that he had grown resentful over what had transpired in the later years. Baelish's love was not only rejected, he was nearly killed by the man that she was to marry instead and IIRC, Cat never attempted to communicate with him after his near death. Such a cold treatment after nearly dying for her could have grown into resentment over the years. It does not seem that Baelish went out of his way to help Catelyn either; Baelish lied to her about the origins of the dagger used on her (leading to a great number of negative occurrences) and plotted the betrayal of her husband, Ned. In my eyes, his courting of Sansa is his final insult against Catelyn, he couldn't have her love, so he will have her daughter's, in spite.