My animation class is trying to use our rigs to do an animation assignment in lifting weights.
The problem being that people are trying to use link constraints to link the weighted objects that we are picking up to things like the hands.  However, it seems that when we link things, there is a sort of a weight to the link (similar to that of a look at constraint) and when we link on say frame 10 and try and move the hand the object that is linked to it, doesn’t seem to want to move with it, or when it does, it moves at half the speed.  And then the farther we scrub away from the frame with the link, the better the link works.
So we have to set several constraints to get the the object to change position, but then it won’t rotate correctly.

Is there some set up that we are missing, or something that isn’t being done that would fix the problem?

Like all animated values in Max, if you set a key on (say) Frame 10, Max will interpolate from frame 0 to frame 10 causing the odd movement you see. Link the object to the world at Frame 9 (and maybe at frame 0) - this locks it to the world until the constraint (on frame 10) takes over.

Couple of points.
Always search the forums first - most questions have already been asked (and answered). This can save you a lot of time.
http://area.autodesk.com/forum/index.php/forums/viewreply/90183/
Put your Max version (and brief system specs) in your sig - quite important with the number of versions of Max there are and the differences between them.

Max 4.2 through 2013.
XP-64 (SP2)
NVidia 9800GTX-512 (Driver 266.58).
Core 2 Quad Q6600 2.4GHz, 8Gb Ram, DX9.0c.

Do you mean Position constraint? AFAIK there isn’t a weight value with link constraint, only a
frame.

If you are using position/orientation constraints, which do have weights, you need to have
two things as targets. One should be a world object (something that doesn’t move and sits at the
start position of the constrained object) and the other would be the hand (or hands).
If you want the link constraint behaviour animate the weight of target one to 0.0 and the weight of
target two to 100.0 over one frame.

Think of the weight value as a percentage between the two targets. If one target is at 100, but the
other is at 10, there is still an influence from both.