This##This is a hold over from the comics, and likely:
It will likely be pseudo-science and/or hand-waved explained in the sequel "Ant-Man and the Wasp".
Update: The ###Update:
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 neutrons add mass
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.
In the atomfirst movie, and"Ant-Man", Hank can no longer use the increased nucleus size makessuit because of continuous damage to his mind over the hold onyears. It's also the electrons weaker, allowingreason he needs the electron ringfull suit, to increase in distanceprotect him from the Particles' side effects. Boom, increased size AND massWhich Cross didn't compensate for in his fever to create the YellowJacket, hence Giantand the Cross Particles (A poor Pym Particle rip-Man's giantyoff) seem to have affected him, turning him into the super-ness and strengthhammy, irrational villain we see at the end. In "Civil War" Scott immediately prefaces his transformation, saying:
"I've only done this once before. And Passed Out. And may tear myself apart trying this."