Voltage problem

What vehicle and what year?

2001 Wrangler sport 6 cyl

Assuming Advanced correctly tested the alternator which is a big assumption what i would do to eliminate grounds or a battery cable/clamp issue is to measure the voltage right at the alternator's output terminal.
Best and safest way to do this is to attach an alligator jumper clip to the terminal with the other end of the jumper going to the +volt meter's probe and the - meter's probe to ground.
(Be careful as the alternator's output terminal is always at B+ potential even with the engine off.)

Then start the engine and see what the voltage is right at the alternator's output terminal.
If its 14+ volts then there's an issue with the battery, battery cables, battery clamps, grounds creating about a 1 volt voltage drop somewhere.
If its still 13.2 volts it could still be a bad ground, alternator itself, alternator's field connector or a bad PCM.

2001 Wrangler Sport 6 cyl.
I have not been getting the voltage I need for my accessories. Tried replacing my alternator with no good results. Still showing 13.3v coming to the battery while hooked up. Need at lease 14v.
Took the new alternator back and had my old alternator checked at Auto Zone. On their bench tester it showed good at 14.7v. Put it back in the Jeep and it still showed 13.3v. Disconnected the battery, while it was running, and it showed well over 14v when accelerator was pressed a little.

Could a weak battery cause the decline in volts from the alternator???

Those older wranglers are notorious for having dirty grounds, particularly the main battery ground that connects from the battery to the engine block.
You can chase that down and try to clean all the connections but easier to buy a 24 inch battery cable and run a redundant ground from the battery to the alternator mounting bolt