When astronomers detect an exoplanet using its transit and calculate its size to be, say twice the earths size, do they have any way of knowing that its actually not a slightly smaller planet with a moon that just adds to the dimming?
To identify any transiting exoplanet you need to observe several transits. One way of trying to identify an exomoon is to see to what extent the transits are identical. If an exomoon was orbiting the exoplanet then, in general, it would be seen at different phases of its orbit during each transit. This would give the transit a slightly different shape/depth because the exomoon would either transit before, after or at the same time as the exoplanet. These effects are sensitive to the exomoon radius compared with the exoplanet radius.
The other (and more likely) technique is to study timing variations in the midpoint of the transit. It is the centre of mass of the exoplanet-exomoon system that will transit on a regular period. The "centre of light", as it were, or rather the centre of the eclipsing area will be located at a different position and so there will be transit timing variations that are characteristic of an exomoon. A complementary technique is that the duration of transits can show variations with time caused by the moon periodically accelerating and decelerating its parent planet in its orbit around the star. And there is an even smaller effect where the distance of the planet to the star varies slightly as the exomoon orbits and this changes the apparent "impact parameter" of the transit as seen from the Earth and therefore the transit duration. These techniques are sensitive to the exomoon mass.
A review of the techniques, including the dependencies on exomoon mass, radius and period can be found in Kipping et al. (2012), however all of these effects are extremely small and to date there is no convincing detection. They are also confounded by things like starspots which cause extra "noise" in light curves and which may mimic exomoons.
The lack of detection may not be surprising. It is estimated that Kepler light curves (the best in the game) might be capable of finding exomoons of mass or radius similar to that of the Earth. Of course, no such moons exist in our solar system... but you could have said something similar about hot Jupiters.