Include the David leg in your flight reservation.
Do not make a separate reservation for the Tocumen airport (PTY) to David leg.
FYI: Copa Airlines is the only carrier that flies from Panama City Tocumen International airport to David. You can find out more about flying from Panama City to David.
Normally, Copa allows you only 1 checked bag of 20 kilos (44 lbs) on its flight to David.
However, if you have a reservation through to David, Copa will abide by whatever baggage allowance your flight from outside of Panama allowed. Most airlines coming to Panama allow bags of up to 50 lbs and often allow up to 2 bags.
However, you must fly out of Tocumen airport within 24 hours of your plane's arrival in Panama City for the other flight's baggage allowance to be honored.
I hope this tip saves you some trouble and money.
If you are going to Puerto Armuelles from David, I have described how to get from David to Puerto Armuelles on my site.