Does using stonger soaps help me lose weight?
I'm afraid no: you are applying a chemical principle to a complex biological response.
The Le Chatelier principle state:

If a chemical system at equilibrium experiences a change in concentration, temperature, volume, or partial pressure, then the equilibrium shifts to counteract the imposed change and a new equilibrium is established.

We start with the definition of chemical system at equilibrium :

the temperature dependent condition in which chemical species are present at concentrations which have no further tendency to change with time.

So what you need are chemical species: molecules, ions. Although fatty acids could be a product &quot;body&quot; is not a compound or a molecule. So what you have is not a chemical system but a biological one. You could go a little more close if you think something like this:
$$\ce{Fatty acid &lt;=&gt; Chemical  \space Precursor_{Y} + Chemical \space Percursor_{X}}$$
However even this is a wrong oversimplification of many complex biochemistry reactions and equilibria.
Moreover you can't interact with these equilibria, perturbing them and so applying LC principle because sebum, which is a complex mixture of lipids, is stored inside sebaceous glands and is formed by the complete disintegration of the cell it self. So to from new sebum you have to from new sebaceous glands.
Soap simply remove sebum not seabaceous glands, so using stronger soap by the way don't affect sebum production. At this point is clear that is no more chemistry but physiology. In this case an equivalent of Le Chatelier's principle is the homeostasis. However from what I know the diet is one of the main factors that induce sebaceous glands to produce sebum so eat better seems to be the best way to lose weight and sebum!

References
Pub Med Sebaceous gland lipids