This is a hold over from the comics:
It will likely be pseudo-science and/or hand-waved explained in the sequel "Ant-Man and the Wasp".
The comic logic is that Pym Particles allow you to change your size. When growing, they pull extra mass from another dimension. Pym, or in this case Scott, gains mass when growing, hence he has increased strength proportional to his size.
How this works in the movies is hard to say, as the movie shrinking is done by closing the distance between atoms without losing any mass. The opposite wouldn't exactly work as you explain it. If they simply increased the distance between atoms, Pym or Lang would atomize into a cloud of separate atoms. Bye bye Ant-Man. It would require increasing the distance AND changing the physics of the basic atomic forces that hold atoms together, making Giant-Man a god in that he would control the basic force of creation. So there must be a separate explanation beyond what has been explained before.
Maybe they will tie it into the Infinity War super-plot, and explain that Pym Particles come from studying an Infinity Stone, which would explain their physics changing power.
The Physics Consultant for Ant-Man, the highly credited Dr. Spiros Michalakis of Cal-Tech's Institute for Quantum Information and Matter, provides a somewhat real life explanation for both the shrinking and growing, by way of neutrino radiation to change the property of the atoms. For Shrinking, bombard the electrons of an atom, changing them into muons, a heavier version with the same chemical properties, the electron rings shrink 200 times in size, effectively lowering the size of the atom, and thus the size between atoms, without any change in mass. For growing, the radiation is used to change protons into neutrons and adding more protons to compensate.
The only mechanism I can think of right now, using the same Pym particles, would be to use neutrinos again, but of a longer wavelength that would make them transparent to electrons. The neutrinos could then travel all the way to the nucleus, colliding with protons to create neutrons plus positrons. The neutrons, lacking charge, would not be able to hold the electrons as close, thus increasing the size of the object. The positrons would fly out of the nucleus and collide with hydrogen atoms (which the suit would supply), thus producing protons (positron plus electron equals gamma rays which go out to space), which can be incorporated back into the enlarged atoms to provide the correct number of protons in the nucleus (since a bunch of them already transformed into neutrons). This process would continue until each atom in his body was converted into a stable heavy isotope of the original (same number of protons and electrons but a bunch more neutrons). Size (due to neutron shielding of electrons from protons) and mass (due to the fact that neutrons and protons are responsible for our mass) would go up. Voila."
Boom, increased size AND mass, hence Giant-Man's gianty-ness and strength. Some comic-physics properties of the Pym Particles would compensate for all the dangerous to Scott part (Radiation, energy requirements, etc).
Not that Pym Particles are completely safe, big or small:
In the first movie, "Ant-Man", Hank can no longer use the suit because of continuous damage to his mind over the years. It's also the reason he needs the full suit, to protect him from the Particles' side effects. Which Cross didn't compensate for in his fever to create the YellowJacket, and the Cross Particles (A poor Pym Particle rip-off) seem to have affected him, turning him into the super-hammy, irrational villain we see at the end. In "Civil War" Scott immediately prefaces his transformation, saying:
Ant-Man: I got something kind of big, but I can't hold it very long.
Ant-Man: On my signal, run like hell.
Ant-Man: And if I tear myself in half, don't come back for me.
Team-Cap Member: He's tearing himself in half?
Other Team-Cap Member: You're sure about this guy?
Ant-Man: I do it all the time.
I mean once...
... in a lab.
And I passed out.