reasoning

What's the reasoning behind the tattoo.

The "reasoning" behind the tattoo is the intention, significance or purpose.  Notice the following:

1. There is usually reasoning behind his actions.
   
2. What was your reasoning in call me tonight?
   

design

I designed the tattoo myself.

To "design" something is to plan how it will look and make a sketch of drawing of that plan.  Notice the following:

1. Who designed this building?
   
2. He started designing clothes when he was 15 years old.
   

sketch

Did it hurt when the tattoo was being sketched into your body?

A "sketch" is an initial drawing of something.  It is usually not as detailed or clear as a finished product.  Notice the following:

1. Can you make a sketch of your plan?
   
2. She is always sketching in her notebook rather than taking notes in class.
   

vary

Tattoos can vary in amounts of pain.

If the pain of tattoos "varies" then it changes depending on the person and the location on the body.  Notice the following:

1. Her attitude varies from one day to the next.
   
2. The temperature is basically the same all year.  It doesn't vary much.
   

meat

Because there's not much meat on the chest.

We use "meat" informally refer to muscle or sometimes fat on the body.  Notice the following:

1. My grandmother is always trying to put meat on my bones.
   
2. It was a good thing the dog bit me in the leg where I have a little more meat.