Answer:
Looks like water, but it's heat. Sits on sand, lays on concrete. A play on the eyes, but it's all lies.
I have an eye but cannot see, You'll head inside when you see me.
What stays the same size no matter how much they weight?
A beggar's brother went out to sea and drowned. But the man who drowned had no brother. Who was the beggar to the man who drowned?
I'm white, I'm round, but not always around. Sometimes you see me, sometimes you don't.
People take me on walks and I run and have fun. What am I?