Pro Mite 15/20

I've got a 1986 Chris Craft Scorpion 266 with twin 3.0 Mercs. I de-winterized the boat three weeks ago and it started up just fine. This past Saturday I was going to take it out and both batteries were too weak to start the motors.:facepalm: At first I thought there was something wrong with the charger, which can charge three batteries and which I leave on all the time when I'm on shore power. I checked the voltage and it was putting out ~13.4 volts, but I did notice the housing on the charger was very warm to the touch. Almost hot. Is this normal? Anyway, one battery seemed weak at about 12.2 volts, but the other newer battery was reading around 13.2. I cleaned the terminals( which were oxidized, but not too bad), and left the charger on overnight to see if maybe it was a connection issue. The next day I tried again. The motor with the stronger battery actually started and ran for a few seconds, but died and the battery was too weak to turn it over a second time. The motor with the weaker battery was exactly the same, and this battery is the one that furnishes power to my bilge pump, blower, and radio.

So, yesterday I pulled both batteries and had them tested. Sure enough, the weaker battery was bad with like 10 cranking amps instead of 650, but the stronger battery was still fine. (only 6 months old). I'm about to install both batteries again but I don't understand why the stronger battery would not turn the motor over. It had more than enough power. Is it that it somehow works in conjunction with the other battery?

Thanks.