I have a 12V 450AH battery system (4 Rolls golf-cart-size). It's going on 5 years old. It's mostly a PV-powered backup power system so the batteries are rarely discharged deeply. Recently I got a different MPPT charge controller that once an hour or so does a "sweep" trying out all possible voltages at full power. With 360W nominal PV power, on a sunny afternoon, starting with the batteries at a bit above 14V, that sweep, which takes close to 20 seconds and forces about a 20A charge current, brings the voltage up over 15V. That makes the over-voltage alarm sound in my inverter.
Is that a sign of weak batteries - or a sign of full healthy batteries?
As a test, I've turned on the charger function of my big inverter. Using grid power, I have that set to a current limit of 45A. Starting in the evening (no solar input) with the batteries at about 13V, over a couple of minutes the current gradually decreased to about 20A, while the voltage increased to 14.2V (the charger's bulk mode voltage limit) and stayed there. So it seems that when not bubbling with hours of solar input, the batteries are not quite as quick to rise to an unreasonable voltage.
Other tests: with an evening load of about 5A it takes several hours for the voltage to decay to around 12.4. With bigger loads (up to 20A) it dips somewhat lower but bounces back when the load is removed.