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Why is the usual percent concentration of a concentrated acid's solution similar to its molar mass?

For example:

                FW (amu)     mass %
sulfuric        98.08        98%
nitric          63.00        68%
hydrochloric    36.46        36%

Is there some reason for this similarity or is it coincidence?

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Because of its solubility. More concentrated solutions of, for example, nitric acid or hydrochloric acid, will result in fuming solutions where acid concentration evaporate out until the solution reaches an equilibrium. Do not get confused. You can actually dissolve more than 370g of hydrochloirc acid in 630 mL of water. In effect:

Solubility in water (Wikipedia)

823 g/L (0 °C)

720 g/L (20 °C)

561 g/L (60 °C)

But if we talk about a commercial solution, which should stay at the same concentration in time, you need to find a compromise between most quantity of acid possible in solution and less lose of acid due to vaporization.

Remember that pure hydrogen chloride is a gas at room temperature. If you continue increasing its concentration, you end up with man equilibrium shifted towards gas phase.

Also, as you can see, if you increase the temperature, solubility decreases, so if you heat a 50% aqueous solution of hydrochloric acid, you would end up not knowing what quantity of the reactant are you actually using.

Nitric acid is less volatile, and sulphuric acid is much less volatile, so you can have the latter almost in a pure form (98% is not an aqueous solution anymore! is just sulphuric acid with some water and other trace compounds)

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