There are three types of padded suits (or Fat suits):

1st Pillow padding.
2nd Batted padding.
3rd Structured foam padding.

Pillow padding:

The easiest to make is pillow suit and is exactly as it is named, several small oval-ish pillows are made thin and placed at key points on the body (Belly, Thighs, Butt, etc.) The pillows are affixed with thread to a lycra dive suit under-suit, and is separate from the outer suit (the fur).

This suit is a pillow-padding suit:

Batted padding:

The Batted suit is next, and is made of ½"quilt batting layered to gain thickness, and spray glued to a liner. The liner and then is lose lop stitched on to the inside of the outer suit, or can be covered and made into a body pillow separate from the outer suit. This suit has a Batted Suit:

This suit is separate from the outer suit, Te the bunny (the example above) is a cross between the batted suit and the foam-structured suit, and his lining is fixed permanently to the inside. The front of the legs are foam, but the hips, and rump are batting:

Structured foam padding:

The last is foam-structured suit, the hardest to make. This padded suit is made by gluing shaped strips of ½" to 1" foam side to side. This requires a bit of math, lots of experimenting, and a dummy to work off of. Then a little batting helps support the foam, and all is glued and sewn onto a lining. With really big anatomy changes like the example below, I also put removable polyethylene tube hoops in the lining under the foam around the mid-section. This keeps the suit extremely lightweight, breathable, and study. If you are going to make the padding removable cover the foam in tight thin costumers nylon, and sew the lining to that. If not just sew the lining onto the backside of the outer suit. The latter is much harder to clean, but is less likely to bunch, or move out of place.

A work in progress:

All the suits on this site are custom made patterns that I make to help them lay and move on the padding better. Dummies help a great deal in placing of padding on the suit, and I suggest either making Duct Tape dummies, or get a mannequin or something. There are many different ways to do this, and I have a rule that "Anything Goes", if it gets my to a satisfactory end. Experiment, Experiment, Experiment, and if you mess up it can be fixed. Trust me…

I hope this is helpful.
Enjoy