Can there be a string so thin as to be invisible, but that can still support a visible weight? A spider web thread is very thin, yet it can support a spider. Given that the human eye visual acuity is finite, are there materials, natural or man-made, sufficiently thin that a string made from such material could support a visible object, yet be invisible from up close?
Clarifications:


*

*the string is "invisible" if a human with normal vision cannot notice it from a distance of 50 centimeters, against a black background in high-contrast conditions (strong lighting shining in its direction).

*the object suspended from the string is "visible" if the same observer, in the same conditions, can see it. Any material could be used, which presumably suggests ultralight materials such as aerogel.


An obvious application would be stage magic, but I suspect there might be more useful ones as well.
 A: Carbon nanotubes, or similarly manmade materials, might be able to accomplish this in the future.  The current record is a tensile strength of 63$\times$10$^{9}$ Pa (Pa = pascals = N/m$^{2}$ or force per area).  So if we assume a circular cross section, then the area is defined by 4$\pi$r$^{2}$.  We can take the tensile strength and the area formula to find the radius needed to hold a 1 kg mass to be r ~ 10$^{-6}$ m or ~1 $\mu$m.  This is ~50-75 times thiner than a human hair, depending on the hair.
Though a person may be able to see such a thin object at close distances, I doubt one would be able to resolve such a thin strand from more than a few fee away.  One test you could do is to hang a human hair (make sure it is taught) and slowly step back until you cannot see it.  To zeroth order, the distance from which you will no longer see our hypothetical nanotube above should be ~50-75 times smaller.
A: Yes, of course this can be done because a suspended object can have larger dimension than the diameter of a string holding it.  In fact, the minimum dimension of a suspended object can be many times the diameter of a string suspending it at 1 g.
Note that it is this relative size that matters, not the absolute sizes.  Since human visual acuity is finite, as you say, at some distance the string will be invisible but a larger object suspended from the string still visible.  You could easily suspend a beach ball, let's say 500 mm in diameter, from a thread only 500 µm in diameter.  That gives you a 1000:1 dimension ratio, so there will be quite a large distance range over which the string is invisible but the beach ball visible.
Additional factors determine "visible" than just size.  Light reflection or emission can change the visibility of something.  For example, if the beach ball was internally lit so that it appeared to glow, a much larger diffuse black string than in the example above would still be inivisible in low ambient light.  Conversely, if the string were made of something shiny and reflective and viewed against a black background, you would see the string due to the additional light coming from it, even though its dimension is too small to resolve by itself from your viewing distance.  This could even make the string visible at a distance the beach ball is invisible.
A great proof of the latter is that you can see stars other than our sun.  The apparent size of distant stars is way too small to resolve with your eye when viewed here on earth, but yet you "see" them due to the extra light they emit relative to the background.
