No no, splitting hairs is acceptable and welcomed, so thankyou sound.
It's exploring, getting into a thing, and I always enjoy and am enthusiastic to do so.
And upon you doing so it has revealed the error of the usage of that as an example.

Let me offer, upon reflection, a better example and answer to your enquiry.
~smiles~ Well I hope it's better. As I observe it, it looks way better.

Bin the overweight part because that is not part of my reality.

I am skinny, always have been. Whilst growing up, I never paid no heed to my physical appearance till my late pre teens and beyond.
I began to feel shame because men are big and strong and musclely, and I was becoming aware that I did not have that.
It's not only girls that have body image issues.

It quickly developed into such deep shame that it was painful to go swimming in public, with family I was ok.
Teens to 20's I would not wear shorts.
It never occured to me to do weights to build my body up.
My life for many years was a self feeding cycle that perpetuated the low self esteem.
Can't build the body up and like myself as that contradicts the worthless belief that was buried deep within.

So, during those years, if someone made fun of my skinny body, it would hurt deep, because it hit the wound, it exposed the shame.
Mid 30's was when I started the serious self exploring, and after many issues were sorted, it dawned on me that I actually like my skinny body.

Now, insults or jokes about it have no affect because I carry no wounds or shame of it.
Now, if someone said I was skinny, with intent to insult, I would simply congratulate them on their powers of observation,
and would then ask do they have issues with skinniness.

Regarding desensitivity.
And, it's been two days since reading your post, and the info from observing this word is still coming in.
Pages and pages. The difficulty is containing all this info in the least amount of words possible or choosing what to share.

Sensitivity is the ability to sense. It's neutral and it's only within the context of situations does the classification of good or bad form.
Put your hand next to fire, sensing informs and you pull away = good.
A person flirts with you, your senses translate the info into arousal, you have sex, this ends your marriage = bad.

Sensitivity is strongly linked with awareness. Awareness is the ability to see and understand. Seeing is a sense.
And this seeing is one's inner sight, one's insight. The sixth sense. The ability to see into a thing.
To get into it. To see beyond the range of the other five senses.
Sensitivity is needed to progress. To sense something is to be aware of it.

Being less sensitive can come from two opposing directions.
If an inner wound has been healed, you no longer feel pain there.
Erecting a defence around the self also produces less pain. Build a solid enough wall and no pain is felt. The thick skinned thing.

However, both ways are not a reduction in sensitivity. In both cases, the sensitivity, the ability to sense, is still the same.
The former produces less sensation because the wound is healed, and the latter produces less because nothing can touch the wound.
The only reason to form a thick skin is to protect self from harm, usually because harm has already been experienced.
The sensations/feelings have reduced but not the ability to sense - one's sensitivity.

There are several pros and cons to both ways, but I look at the end result.
With a wall, pain is reduced quickly, but healing is never achieved, one only thinks all is well.
With the other, it takes a lot longer to reduce the feelings, but eventually one is truly healed.

The dark night of the soul, the walking through the valley of shadow and death scenarios, they are by my experiences,
a person choosing to heal themself instead of hiding behind the safety of the wall.
Once healed, walls are no longer needed. Once healed, externals no longer affect or influence permanent change within.

But in order to take this journey and be successful at it, one must be keenly sensitive to see and feel the wounds that need healing.
But in doing so, it becomes a painful journey.
The wounds have to be touched, explored, gone into, understood. This is a painful process.
But as the journey progresses, the pain reduces as each wound is healed and pain gives way to enthusiasm and joy,
excitement of what will be the next wound to heal.

The more walls that are removed, the more freedom one has.
There is pain behind the wall, but compared to what one sees beyond the wall, the devastation of accumilated wounds, the pain behind the wall is small.
Venturing out beyond the relative comfort can be daunting. I ran back to my safe house many many times on my journey.
But each time I did venture out, I increased in understanding, courage, etc, within each tiny step.
15 years of one step at a time and I have arrived at a place of immense beauty, wonder and freedom.

~smiles~ Went off with the faeries again.
Work out the mechanism of your desensitivity. Look below the feelings, the sensations. Look and you will see.