Right, so now for some math, to show the hidden bonuses.
We have my weapon grid, as you can see it's 13348 total attack power.
Then we have my eidolon grid with 9098 total attack power
Then we have the hime's total attack power
So, let's take a look at Gabriel for example.
If you take the 4890 attack power that's listed for her and add it with the both grid attack powers.
4890 + 9098 + 13348
We get 27336, which is a bit less than the displayed attack power for her at 27879.
So, where is that missing attack power?
Eidolons supposedly have a 1.1x multiplier if they are the same element as the members of your team.
So if we take Jormy and Rahab's attack
1887 + 1704
We get 3591 and multiply it by 1.1x which gives us 3950.1
So if we subtract the 3591 from the 3950 we get 359 and add that to the eidolon total power giving us 9457.
So now we take a look at the weapon grid.
Nike, Gabriel, Apsara, and Belphegor all have arcane orb as a preferred weapon.
Coincidentally there is 1 arcane orb on my grid.
So if you take that 929 and multiply it by the 1.2x bonus for preferred weapon type, we get 1114.8.
Subtract that and we end up with 185.8.
Then we add that number to the weapon grid total attack power which gives us 13533.
So now we have our new numbers for the attack power of our weapon grid and eidolon grid.
So we take 13533 + 9457 and end up with 22990.
So now, looking back at Gabriel's attack power
22990 + 4890 = 27880 which more or less matches what is displayed on the character page.
So if we take nike's stats
22990 + 3978 = 26968
Then Apsara's stats
22990 + 4600 = 27590
And lastly Belphegor's stats
22990 + 5092 = 28082
Of course all of these are off by exactly one, but that's likely just an issue of +s being a fraction and were just rounded.
As you can see though, it's a pretty insignificant amount at this point of the game and not really something you need to worry about until super late game when you have several maxed SSRs.