Terminal 8

This is what you have to do :
-clearing immigration
-picking up your bags
-clearing US customs
-transferring the bags at AA connecting flights counter
-clearing security
Then look for your gate for the flight to LAX.
JFK_E

Sometimes the check-in agents let you "slide" with 2-5 pounds extra, but don't count on this. See if you can relocate some of the heavier items in you carry on bags may be?
Here is the list of shops at T8(just choose Terminal 8 from the tabs):
http://www.panynj.gov/airports/jfk-shops-restaurants-services.html
JFK_E

American charges $100 for an excess weight. And that is per bag.
JFK_E

You will be :
-clearing immigration
-picking up your bags
-clearing US customs
-transferring the bags at AA connecting flights counter
-clearing security
JFK_E

Yes, It is roughly 1hr each way JFK-Manhattan(either by taxi or express bus).
JFK_E

You should be OK as long as you make it at Delta before 2:55pm. Clearing customs takes up to 40 min and between terminals 10-15 min.
Having your Delta boarding pass issued by American and checking the bags through will help you a lot.
JFK_E

You will pick up your bag at T8, domestic baggage claim which is on the first floor of the building. Then you will go to the second floor , follow the signs to the Airtrain and take it on track 2 to Terminal 4.
JFK_E