2001 ford f150 Alternator problem?

2001 Ford F150 XLT 5.4 4x4. Truck runs and drives great, its my work truck. I hooked my boat up to it the other day to pull it out and clean it and left it hooked up over night. Went out next morning truck wouldnt start, battery was weak (the battery is only 3-4 months old) so figured i must have left something on hooked up the charger and fired right up let it run a while and shut it off and it started back up fine. About 4 hours later battery was dead again. (Well weak). Hooked a meter to the battery and said was 12.7. Jumped truck and was reading 19.4. Which i understand is to high let truck run a few minutes to watch the meter never changed shut truck off battery was reading 17.3. Can the over charge from my Alternator cause the battery to die out over time ? Or should i consider looking for a new problem to top this? Alternator will be replaced but should i check anything else? Thanks