General

From my understanding, the larger a person gets the more mass their body has to accommodate. Normally, our natural body structures aren't meant for walking with three to four times its usual weight. Therefore when a really fat person walks, the body has to waddle in order to accommodate the shifting mass and not fall over.

Furthermore, you'll notice waddles a lot more in people whose legs get pretty fat. All that extra padding causes a bit more frictions and leg spread, which makes it a bit more natural feeling to make a slight waddle.

As for penguins, I believe they waddle just due to their very short legs haha. You'll notice that sometimes, they'll actually just hop forward randomly as a way to compensate for their extremely short legs.

But yeah, so waddling is caused by a mixture of a heavier load causing the body to shift to accommodate it, and extra padding causing the legs to spread a bit. Causes that leaning back and forth motion that traditional fat person waddling entails! . Hopefully this helped! If any of my info is wrong, hopefully someone can correct me haha.

My ex gained about 70 lbs while we were together and she waddles now. She said it was an interesting feeling as her thighs got larger that she had to position them around each other when she walked. It's subtle but became more apparent when we were on vacation and she was getting tired from all the walking.