What I'm using right now for an inflated charater is soft-body physics, which is similar to the 'several sprites' method, but instead of sprites it's invisible physics objects tied together with Fixed Joints. The only drawback with my implementation is that the amount of bounciness comes from how precise the physics simulation is. Not precise at all leads to very fun animation for the character, but the physics simulations becomes just about as stable as a coffee shop at a cookie-wafer jenga competition; Things break fast. I've found a good middle ground though. I'm using a flat 3D mesh for the body and changing the verticies to match the position of the physics objects, so that makes things a lot easier on me.
I'll try to get a video of what I've got done so far to show you guys...
Here you go! [VOLUME WARNING]
Sadly, the size of the object cannot be changed dynamically without breaking everything. I'm happy with the results though!
In a way, it's a revisit of what people like most - to see inflated characters, or to see characters inflating - but now from a "how-to?" point of view
Most characters are around 100 pixels high when not inflated and usually within 200-300 pixels when at their absolute limits, a 1920x1080 screen shows a piece of the field which is nomally a 5 seconds run for them
+ Full-body sprites - that's a stop-motion animation. It's easy to change for everyone, fully customizable but huge, and you need extra disk space for every extra animation. Each picture can be gorgeous if a talented artist draws it, each picture stretches smoothly, however picture change is visible and abrupt.
+ Soft curves stretch on uninflated body - that's how Spine, Spriter and the like work. You have several sprites for bodyparts of the character, and you stretch belly and boobs independently of other parts. It doesn't need any extra game size for showing any motions and inflations (like inflating while running, or deflating while rolling), looks perfectly smooth all the way, but is utterly unrealistic even for a fantasy - buttocks won't squish, boobs won't rest on the belly and so on.
+ Spring model - that's like "Tet-a-tet". In an old DOS game of mine ("Tet-a-tet") I have a female body drawn with a single brush stroke looking like a closed pattern. Each straight and curved line of this pattern is an elastic string, "soft parts" like back and bust curves stretch better than "more rigid" spine and toes. It shows inflation perfectly smoothly all the way from uninflated to bursting, has two dozens of parameters which let describing any bodytype at all, and I can copy-paste it from DOS game into Inflation Formation - BUT it's just pattern, it's not a colourful picture. Who would want to look at a stretching of a single brush stroke?
+ Maybe all that is crap, and something entirely different works better in 2D?