How much load can a 2x6 support?
Subsequently, one may also ask, how much weight can you hang from a 2x6?
So the area between two 2x6, 6' long, on 2' intervals would have to be able to support 2x6x40=480 pounds of weight. Actually, slightly more since the formula is for 8'-6" spans but it just gives you a little bit of extra load for just in case.
Also to know is, how far can a 2x6 span without support?
In general terms, joists spaced 16 inches on center can span 1.5 times in feet their depth in inches. A 2x8 up to 12 feet; 2x10 to 15 feet and 2x12 to 18 feet. The larger the deck, the larger the joists.
some of it gets pretty technical in nature, and mostly relates to pounds / square foot of loading. 2x6s are generally used for ceiling joists, esp since you said 24" oc and reallllly short spans only (5 or 6 feet ). Most floor loads would be a minimum of 2x8 @ 16" oc and most preferbaly 2x10.