Strength
Strength goes like area.
Intuitively, the cross sectional area of a muscle counts the number of muscle fibers (actually, myofibrils).
Thus, $S\propto A \propto L^2$.
But mass goes like volume, $M\propto V\propto L^3$.
Therefore strength is proportional to the $2/3$ power of mass,
$$S\propto M^{2/3}.$$
This equation expresses the fact that an increase in mass does not give a proportionate increase in strength.
For example, adding $25\%$ to your mass will increase your strength by about $16\%$, assuming your body composition and neuromuscular skills don't change appreciably.
Relative strength
In addition, we find that relative strength, strength per unit mass, goes like $M^{-1/3}$,
$$\frac{S}{M} \propto M^{-1/3}.$$
Thus, after adding $25\%$ to your mass and getting $16\%$ stronger, you are actually $7\%$ weaker in terms of relative strength.
These facts are known, at least intuitively, to all athletes.
In strength sports, formulas such as these are used to compare athletes across weight classes.
For example the Wilks coefficient is used to ``normalize'' weight lifted.
(In fact the Wilks coefficient is roughly $(50/M)^{2/3}$, where $M$ is the lifter's mass in kilograms.)
The ant
From the above we can also see that relative strength is inversely proportional to $L$,
$$\frac{S}{M} \propto L^{-1}.$$
Thus, a man a hundredth the size of a normal man would be one hundred times more strong in terms of relative strength.
In other words, if a man can lift his bodyweight, the same man a hundredth the height could lift one hundred times his bodyweight.
(What if a normal man were to grow one hundred times in height?
He would be one hundredth as strong in terms of bodyweight, and would be crushed under his own weight.)
It is thus not surprising that an ant can lift many times its bodyweight.
Precisely how much is more a question of biology than physics, since we are comparing not only organisms of different size, but totally different morphology.
Certainly an ant can pull, in relative terms, much more than a human.
In fact, ants have hooks on their feet.
Think of our tiny man who can lift one hundred times his bodyweight dragging himself across a rough surface with climbing gear.
It would not be surprising if he could pull on the order of one hundred times his bodyweight.
Figures
You will find below a plot of strength vs mass and relative strength vs mass, in natural units.
