Develop communication skills. The root cause of inequality in relationships is miscommunication. What are your partner's desires, and more important, what are her frustrations? The more solid an understanding you have about her position, the better equipped you'll be to improve your role in the relationship.
Be careful when accepting gifts/favors from your partner. Everyone loves a surprise gift, but when it becomes a habit, you owe it to yourself to question the motives. Does your partner make more money than you do? Is he trying to barter status in the relationship? If you ask yourself these questions and conclude that it's done out of mere affection, great. If not, then you owe it to yourself to confront your partner.
Be honest and open in sharing your life. Make an effort to introduce her to your friends and family. The more invested she feels in your life, the more willing she'll be to develop a true partnership that is the foundation of an equal relationship.
Never decide on relationship matters without your partner. This is the strongest indicator that you don't take his role seriously. Err on the side of caution and thoroughly discuss the issue, then decide together.
Be willing to make sacrifices for your partner. There will be times when you'll have to give up old habits to make her happy. No one says you have to become a different person, but accept a degree of change. It says you're willing to embrace compromise and that means you're willing to embrace a new life together.
When it comes to money, take note of the little things. If you feel as though he's overextending himself, make an effort to even the score. Never make him feel like the relationship poses an added financial stress.