You're right, there was practically nothing to gain from the marriage. In Robert Massie's biography of Peter, "Peter the Great: His Life and World" he often points to Peter's willfulness and desire to do things his way - e.g. the construction of St. Petersburg, and the Grand Embassy - to show that Peter held little regard for social protocols or historic norms. So it's possible that it was actual affection that prompted the marriage. We'll probably never know the precise "why" though.

Peter was a very impulsive guy and made some extremely strange decisions. I think one good reason, though, is that by marrying a Livonian peasant woman he prevented the choice of his spouse (and hence successor) from being the subject of political rivalry between the traditional boiar clans, who would normally have provided the bride. This was a major problem over the course of the 17th century, and Peter's childhood was repeatedly marked by violent inter-boiar conflict. Choosing Catherine as his wife meant that the new people he brought into the court (like Menshikov) had as much claim over Russia's future as the traditional nobility, and like his edict claiming the right to nominate his own successor, served to force the boiars and their supporters to accept the succession on Peter's terms.