This refers to the fact that our sun has probably increased its luminosity during its lifetime (approximately 3.5 billion years). This assumption is based on astrophysical observations of many other stars. The best scientific conclusions are that when our sun was young it had a luminosity (total energy output) of 70-80% of what it is today; however, there has clearly been (based on geological records and long term evidence for the presence of liquid water) approximately the SAME long term planetary temperature on earth (about 15 degrees C, averaged planet-wide) instead of colder earlier surface temperatures followed later by warmer surface temperatures. This paradox suggests that the planet's surface temperature may have been controlled by atmospheric gas concentrations that varied over time while keeping (via the greenhouse effect) the surface temperature relatively constant (see Gaia hypothesis). [Science; v33n6; 20; 1993.] [The Atmospheric Journal; v98n6; 2268; 1989.] [Science, v177, 52-56; 1972.]

This definition is in context to Atmospheric Chemistry. See more contextual defintions for Weak Sun Paradox.