Here's my theory on how morphing works:
It is said in book 10 that when you morph something small, the extra mass is extruded into Z-space, then retrieved when you demorph. Ax mentions that there is a very small chance that a ship traveling in Z-space could run over the extruded mass. In book 18, an andalite ship really does pass close by the Animorphs' stored mass, resulting in their consciousness getting "shunted" to it. They find themselves in what sure looks like their original bodies.
My theory is that the extruded mass thing happens every time you morph, not just when you morph something small. Your body is sent to Z-space, and an entirely new body of whatever you morphed is constructed to replace it (don't ask me where the mass for the morph comes from; maybe the Andalites shoved a bunch of stuff into Z-space for morphers to draw on). Your body is put into some sort of state that allows it to survive Z-space conditions, but your brain remains partially active. It is linked to the brain of the morph, controlling it and receiving sensory data. When you demorph, it brings your body out of Z-space and sends the morph back. During this process, it detects and repairs any injuries because, well, why not?
This explains why the Animorphs remain sentient even when they morph animals with brains that couldn't possibly support human intelligence. What happened in book 18 was that the ship passing by disrupted their neural link, causing their original bodies to "wake up."
So, to answer the original question, when you demorph, it doesn't rebuild your body from scratch. It just pulls your old one out of storage while taking the opportunity to repair it. So things like weight, level of physical fitness, haircuts, etc. should be unaffected. By the way, we know for certain that haircuts aren't affected. In book 2, Rachel tries to fix a bad haircut as she demorphs, but that doesn't work because "morphing doesn't work that way."
That said, the acquiring process does appear to record more than just DNA. In book 30, Marco acquires some middle-aged guy and when he morphs him, ends up just as fat and out of shape as the original person was.