Overweight items are more likely to be damaged, most often as burst zippers or broken wheels or handles. And those are the things the airline won't pay for, precisely because it's so common. Also remember that if you can't lift it easily, chances are the guys below the wing won't be able to either, which means more chance of rough handling like drops and kicks. Every exterior protrusion (like feet and wheels) is a potential grab point in the confined space of the baggage compartment, so make sure to buy sturdy luggage, preferably with hard plastic handles on all sides and durable inline-skate wheels. I can't even count how many times I've gone to pick up a bag and the handle popped off right in my hand because it was so heavy.
Another note: be sure to put your name and contact details inside the bag. If the handle with the tags comes off during handling, and there's no nametag inside, your bag is now one of a thousand unidentifiable nondescript black roll-aboards in the unclaimed bag warehouse. That's also why it helps to have a bag that stands out, be it a bright colour or pattern, or one of those patterned straps that goes around the bag.
A quick check of aa.com shows that you get one free checked bag per passenger, up to 157 linear centimeters (length plus width plus height) and 23 kilograms (50 lbs) in weight. The second bag costs $60 and it oddly refers you to the reservations telephone line for information on subsequent bags. Overweight or oversize bags between 23 and 32 kilos incur an additional $60 charge. They won't take anything over 32 kilos (70 lbs).
The fees are cumulative. That is, if your second bag is overweight, you're charged $60 for checking it plus another $60 for it being overweight.
As for what not to check, I would never check electronics. The airline won't pay for damage or loss to high-value items like jewelry or electronics. Also, make sure to pack a few days of essentials like toiletries and medications in your hand luggage in case your checked bag decides to go on holiday for a while.
I don't know where you heard that there are no free meals. That may be true for domestic flights, but international flights have meals on board.
(ETA: If your flight is non-stop from PHL to LHR it is not actually an American Airlines flight. It is a codeshare operated by British Airways. If you are changing planes in Chicago, then you're flying on American.)
