Not AU as much as a consequence of narrative: people keep on making bigger clothes for Reiner because after every time he pigs out (or eats people), he gains a few pounds in muscle. There were times when he didn't get new clothes after devouring monthly food supply, and after he digested it, he walked at Bertholdt with a shirt that fit him like second skin... which then started busting at seams when Reiner raised a hand in greeting, thus flexing out of his sleeve. rest of clothes soon followed.
(Agreed, especially if he ended up having large meals frequently, this could be a problem. His green shirt would probably survive the longest, though he probably does this because he’d pop buttons on a button up all the time.)
(His jacket would probably be the first to cause a problem with it getting tighter and tighter making it really hard for him to move around in. (Eren probably takes advantage of this in training and wins a few. It’s a sign to Reiner for new clothes) So like you said, raises a hand or shakes a hand and then their goes the jacket arm ripped to shreds and struggles to take if off and more things start to rip. At the very least ends up shirtless. Could end up even worse (ie better) and have more torn.)