Great tit feeding other great tits?!

We have a hanging feeder with sunflower hearts which about 3 pairs of great tits have been frequenting for the past 3-4 days. I suspect they are nesting in the gardens nearby as it is just minutes before they return to feed.

Sadly a squirrel or (possibly a rat overnight?) got to the feeder in the early hours and there were no seeds left for the tits this morning and they were waiting impatiently

 I left them a plate of seed mix on the ground while I cleaned up the feeder and refilled it

This plate was left under a fairly large rose plant, and I noticed 4 tits. 2 were much fatter and bigger than the other 2. The fatter birds' wings was constantly fluttering, looked like they were shivering (?). The smaller birds picked up bits from the plate and fed the fatter birds, which made no move towards the food but just sat on the rose stems and opened their beaks for the food.

It was cute to watch but confused me as I thought only baby birds are fed? And I always thought fledglings are smaller than parents? Do birds feed each other?