I think there should be a toggle that makes it so your arm is thinner (or not) in the skin section of the account settings page. I recently encountered an issue where i used skin swatch to change my skin to a temporary one (so i wasn't using the default), and that skin had thin arms. When i later changed it to my new skin the thin arms remained and there was no toggle, so i had to change my skin to the default using SkinSwatch TWICE for the arms to return to normal.

I don't know if there are preexisting checks to make arms thinner based on the texture but still, i think a toggle would make this less of a headache.

Arm thickness is entirely decided by the client and is based on the texture file, the website has no bearing on how the client will display your skin.