Non Car Related Question

Wonder if they tested the new batteries?
Back when i sold auto parts,we never tested batteries. Until one bad battery went over the counter. I personally drove 30 miles with a new one and an apology. Never let another battery out without testing it first.that was the only one i ever sold that was defective. Out of 1000 plus units.
Yep, I have gotten 2 bad batteries in a row out of the same store. There were marks on the white plastic cases where they had been banged around and broken some plates in side each battery. The broken plates internally shorted the batteries, and the 1st one almost caught my 1st race car on fire while it was setting in my parents' carport.

OP, I would have guessed a battery with a shorted cell from your initial description. I'd do myself a favor and do what is recommended in post #2: Go get a decent voltmeter; disconnect the charger when it it gets to a steady state charging condition, then disconnect all 6 batteries, and let them 'rest' for an hour. Then test the voltage across the terminals of all 6 batteries, 1 battery at a time. They all should show the same voltage within + or - 0.1 volt. Let us know what you find.

The diagnosis of 'weak' from your battery supplier is not much info. You can learn more yourself with a simple voltage test. Using a battery hydrometer is another step of diagnosis.