Balloons deflate when gas leaks out of them. A helium-filled balloon leaks more quickly than one filled with air, because helium atoms are extremely tiny and slip through microscopic pores in the latex rubber.
Lighter-than-air balloons float for the same reason that an empty plastic bottle floats in water, displacement. Any object placed into a fluid, a liquid or gas, displaces an amount of that fluid equal to its volume, that is, it literally pushes the fluid away in all directions. If the object weighs less than the same volume of fluid weighs, it floats upwards through the fluid until it reaches the surface. This principle is known as buoyancy.
Helium's diminutive size explains why it is lighter than air. The helium atom contains only two protons, two neutrons and two electrons, giving helium an atomic weight of 4 compared with nitrogen's 14 and oxygen's 16. (Nitrogen and oxygen make up 99 percent of the Earth's atmosphere.) For each of these gases, however, a given volume contains approximately the same number of atoms. One liter of helium weighs just 0.1785 grams, versus 1.2506 grams per liter for nitrogen.
The pores in latex rubber vary in size, depending on the manufacturing tolerances. "Helium-grade" balloons feature smaller pores than conventional rubber balloons.