The phrase "if you're happy, I'm happy" is an expression of support and care for someone else's well-being and happiness. When someone says this, they are conveying that their own happiness is closely connected to the happiness of the person they are addressing.
It implies that the speaker's primary concern is the other person's happiness and that seeing the other person happy brings joy and contentment to them as well. Essentially, it suggests that the happiness of the other person directly impacts the speaker's emotional state in a positive way.
This expression is often used in relationships, friendships, and close connections between people to show empathy, understanding, and a willingness to prioritize the other person's happiness. It indicates a selfless and compassionate attitude, where one person's happiness is seen as a shared experience, and their well-being is valued and cherished by the other person.