I have my Weapon’s power at 125, but nothing I and to my ship pushes it beyond that, is that the new maximum?

125 has been the maximum since closed beta.

100 is the max 'standard' setting, while the max setting with boosts such as Transfer Power to Shields is 125. I think there used to be a 'hard cap' of 135, even though it would still read 125, but I don't think it's like that anymore.

With the right skill allocations, power settings, and equipment, you can get yourself up to 125 easily. My Intrepid refit is constantly running at full auxiliary power.

Here is a question, what is the maximum allowed for NPC units?

There used to be no hard cap for weapons power. You could push it all the way to 195. This only ever offset multiple weapons drain; damage was still treated at 125 if you were above that.

The hard cap now is 135 (just enough that a well Specced Nadion Inversion can completely offset 8 energy weapons).