CI gives you very little, and what it gives you is mostly categorically broken. The total lack of post-redirect-get and insane choices on the session data front meant I was using a custom session storage library I wrote instead of the bundled one.

We had issues where the router and loader were not playing nicely at all - we were using the 404 override option in order to do some custom routing (as the router was not flexible enough for even a very basic CMS). However because of how messy the routing code is, and how much of a hack the 404 override was (last time I checked there were several open bugs regarding this on their tracker, some over a year old and completely untouched), it completely blitzed the loaded libraries, so we had to add in more hacks to dodgily clear the cache of loaded libraries and re-run the loader in order to have them available. The only other way to do this would have been to modify the core loader to fix the bug there (but we didn't want to modify core code to make it easier to keep up to date with framework changes), or completely rewrite the router (which really needs to be done, it's a mess).

The database abstraction code is very kludgy and basically useless for anything beyond utterly, utterly basic use cases (there's a reason it's low overhead - it's low everything, including functionality!)

That's just a few of the things we ran into. By the time we went to production I estimate that out of the maybe 30% of CodeIgniter we were actually using for our project, I had re-implemented as custom libraries maybe a third of that amount just to get some sane behaviour, and work around long-standing bugs. Overall I got the feeling that the framework had no solid direction, some of the core components (most critically the loader and router) were quite obviously piles of hacks rather than having been designed and engineered, and honestly the framework was not really much more re-usable or robust than our own custom in-house one. I know it's a very common developer hubris to think you could write your own framework and do a better job, but in the case of CodeIgniter I can confidently make that claim.

On the more technical and abstract side, it's insane that it doesn't use standard PSR loading (so any other library you want to use you have to write a custom wrapper), and the guidance on making re-usable libraries / modules / packages (I can't even remember the right terminology, they use these words in strange ways) is... unclear at best. It uses globals, it's tightly coupled, everything a decent framework should categorically not be. Overall I would say that the level of technical ability on people using and contributing to CI is very low, and most people I've spoken to that think it's great haven't actually used any other framework (which is, frankly, endemic of a large portion of the PHP-using world)

Edit: Also if you care about overhead, you're not writing what I would call a small to medium sized application! Any framework out there worth its salt (and many that are not) will be able to run your application just fine, it's extremely unlikely that the PHP layer will be the bottleneck unless you're writing really terrible code or using a really terrible framework.