I live in NJ, but only worked for a few weeks in NY city and rest of income came from NJ. Why I had to filled out all my federal income in NY state tax form? It is unfair to report my most of federal income which has nothing to do with NY source in NY state tax form.

Can someone help me to understand or explain this?

You will file NY return as nonresident and report only the income you earned while you worked in NY.
On NJ tax return you will report your worldwide income including NY income. Claim credit for taxes paid to NY. Your U.S. Tax Return: Working or Living in Two or More states (http://taxipay.blogspot.com/2008/06/working-in-two-or-more-states.html)