I understand that strings have a size of roughly the Planck length $l_P$ of $10^{-35}$ m.
If that is the case then one would expect that their mass would be roughly the Planck mass which is an enormous $10^{19}$ GeV.
(Strings that have small spins, like standard model particles, are about $l_P$ in length see https://physics.stackexchange.com/a/315166/22307)
In order to model the particles of the standard model their effective mass must be much smaller than the Planck mass.
Is the intrinsic Planck mass of a string largely cancelled by its negative gravitational binding energy so that its net mass is small?
For example assume that the gravitational binding energy of a string is roughly equal to its intrinsic mass energy then we have
$$\frac{GM^2}{R}\sim Mc^2$$
For a quantum object the uncertainty principle gives us the relationship
$$Mc\ R \sim \hbar$$
(I'm assuming a particle model such that its effective rest mass $M$ is entirely due to its internal momentum $P=Mc$ i.e. a zero rest mass particle confined to move around at the speed of light inside a box of size $R$)
Thus we find that
$$R \sim \sqrt{\frac{\hbar G}{c^3}} \sim l_P$$
Therefore, due to negative gravitational binding energy, Planck length strings are effectively massless. Thus they can reasonably model low-spin standard model particles which are very light compared to the Planck mass.
