Pity and compassion are two different things. When you pity someone, you assume that their life's circumstances won't get better. Yet, because life is based on change, this may be a faulty assumption.
When you experience compassion, you realize that this specific individual, is on their own path. They are learning their own lessons meant for them. They can either learn or choose not to. Even if someone seems to be in pain, they may be learning how not to cause others pain. When one is poor, that may be a lesson that shows them that tangible possessions are not everything there is. When someone is dying, you realize that everyone is mortal.
Rather than cry for them, you may decide to become involved in things that alleviate other's suffering to an extent. You know you wont' save them; that's something they'd have to do for themselves over time. But what you do, is love and become proactive. If you see a beggar on the street, perhaps you could ask them how they've gotten to this point. Did they lose their job, are they mentally disabled, etc. You can then help them get connected w/ the resources in their area such as shelters, group homes, community mental health, etc.
To change your emotions (crying), it would be helpful to change your thoughts. Thoughts evoke emotions. What one things is not always correct. Meaning, when you see someone being unfortunate, perhaps through that hardship, that individual is becoming better in some way. Each person has their own lessons to learn in life. Some do it faster than others. This is so because of their free will.