actually the exp you get in Inn was based on your sidequest, so you would have to do sidequest to get more exp at inn

I'm pretty sure it's a bonus exp you get based on the exp you win by normal fighting and questing. I mean, I got some nice inn exp boosts without doing side quests. Some of the boosts were pretty insane (I was close to 10 levels below some enemies at the mid-chapters lol). 

So I'm a bit confused; got up to the part in chapter 4 where Morag says she'll join forces with you to find Lila, but hang on, wasn't she trying to capture us to secure the Aegis? Why is that not a goal of hers any more?

I don;t think so, I got some today without doing a sidequest.

I'll give you my own opinion, but I'm pretty sure that Morag changed her mind once she met Rex about capturing them. She (and a lot of people in the game) thinks that the Aegis can be pretty dangerous on the wrong hands, but it's hard not to find Rex likable and gentle. It's not like her primary goal is to capture Rex to secure the Aegis, but she'd do it if she needs to. So she's taking more of an observer role, once they shared a common goal. But I think she goes deeper on that lately. There's more to it, I can remember one other reason but I won't spoil it because I'm not pretty sure if she said it yet xD. 

EDIT: Oh, also, she noticed the both times they met that Rex was holding back. So she clearly thinks that Rex is, maybe, not a bad fit at all for the Aegis. You might probably think that Mor Ardain wants the Aegis to get more power, but the game is normally ambiguous about that, some people want her for power, some of them are just scared of what she can do.

We really need a thread to talk about characters and plot though xD.

Yep.  It's also a great way of implementing dificulty selection after a fashion as you can chose to make the game easier at pretty much any time by capitalizing on the bonus exp you earn doing sidequests and fighting.  

HOLY SHITTTTTTTTTTTTTTT

THERE'S A CHARACTER IN THIS GAME WHO RECOVERS FROM HIS AMNESIA THROUGH CHILD ABUSE


HAAAAAAAAAHAHAHHAHHAHHHHHHHHHHHHHHHAHHAA

I said no spoilers!

I haven't gotten to that part yet.

Oh, common dude.

It's not a spoiler

It's a minor character in a sidequest who literally does not matter at all and you probably won't remember them

That's not something anybody can know. It helps to use spoiler tags just in case.