take mathematician's approach to simplfy the complicated system.
Assume the two types of people, slim and fat, as two skin covered meat balls with identical internal structure, but with different radii, and hence different surface areas. www.ddhw.com
Because of ...., and.... hence...... therefore the slim one is more sensitive.
First of all, you have to take into account some physiological factors, including whether or not nervous tissue could grow into the layer of hypodermal fat... and the distribution of the nerves in different tissue types, fat and muscle... Second, you have to make sure the speed at which the signals excited by the stimuli transmit from the surface to the nerve centre and the brain stays unchanged across the fat and the muscles... Then count in the radii and surface areas factors... Just assume that your presumption of homogeneous skin-covered meat balls holds...
Your conclusion might be wrong, as I reckon nerves could grow very well in the hypodermal fat, otherwise fat people would miserably lose their sense of touch.... and God knows the signals could not travel faster in fat tissues?
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Well.... It might be easier to make an investigation, get the statistical data, put them into the SPSS, and fix a regression model, get the coefficients, then you will know....