I have a hefty 2x2x4 inch neodymium magnet with poles on opposite
sides. It can easily lift 100Ibs.

1) If my magnet could lift 100kg using the south pole (2"x2" area),
approximately how much could a 2x2x8 magnet made of the same material
lift? What about a 2x2x126000 inch magnet? Does that proportion hold
at any scale?

2) I take one of those classic 5-pound circular disc/plate/barbell
weights and put the magnet where the hole is for the barbell (very
carefully and using well-planned methods!). On the other side of the
weight plate, where the hole is for the barbell, it seems that even
though I have a clear line of sight to the extrodinarily powerful
magnet, that the field has been catastrophically reduced by the
surrounding metal... if I hold a metal ball the exact same distance
away from the magnet, I won't feel the magnet have an intense of a
tug. Is my feeling accurate? If so, how has the magnet changed? Is it
now as if the entire 5-pound weight is the north pole of the magnet,
reduced in power proportional to its mass and reduced in intensity
over the surface area of the weight?

1)  Yes.  the power of the magnet will increase,
           and will be APROXIMATELY proportional to the cross-section.

2) The magnet did not change. Magnetic field around the magnet changes
   whenever you bring a new (magnetic) object to the area (and it does it
   with speed of light = quickly). The 'pull' depends on the magnetic field
   at the location of the object.

    Exact solution eo equations which describe  the field is complex,
    but notion of 'magnetic flux' 
    gives a simple and intuitive APROXIMATION to the field and forces:

   One has to imagine a circuit, as if 'something' (flux) is flowing from one
   pole to another. In this analogy, air has high resistance, iron low, and
   flux (as current would) tries to go by path of low resistance.

Here is the picture of the fluxlines:
 
 www.magnetweb.com/ Sect4A.htm

Ignore the stuff on magnetisation. Picture of fluxlines is an example we want.

If you put a piece of iron in the gap and are pulling it out,
 you are increasing the 'resistance'. That is resisted by the magnetic force
(as if the fluxlines are rubber bands).
 
SEARCH TERMS : magnetic circuits

references 
http://en.wikipedia.org/wiki/Magnetic_circuit 

More examples of flux lines

[
 http://images.google.com/images?svnum=10&hl=en&safe=off&client=opera&rls=en&q=magnetic+field&spell=1
]

 Rating appreciated.

Hedgie

Very fascinating stuff. I wasn't aware that magnets have a "circuit
design" acting similarly to electric circuits. The links were
interesting. Thanks!

Sorry for not producting a picture, but:

The reason a sheet of metal is both attracted to a magnet and blocks
magnetic field from propagating beyond it is because a sheet of metal
causes the magnetic field lines to bend and travel INSIDE the metal.
Go find a good picture and you will understand it.