>I am curious to learn about speaker cabinet design and how important does the cabinet contribute to the overall sound.
It's significant.
>Does the weight of the cabinet make a difference.
Weight and stiffness determine resonance amplitude, with stiffness going up with the cube of thickness. Obviously a thick enough brace will out-do uniformly thicker material but involve higher labor costs.
You really want to limit un-braced lengths enough to push resonances out of the driver pass-bands.
Siegfried Linkwitz has suggested that (mid-range) enclosures shouldn't have over 4 square inches of unbraced cabinet.
>For instance a floor standing speaker that weighs 200 pound versus one that weighs 60 pounds or 300. Is there any correlation to weight and sound? How about material?
All else equal there may be. There's an AES paper which gives an example of cylindrical enclosures (the material is stressed only in tension) being as stiff as 4" concrete which you can (I did that with Siegfried's Pluto design) exploit to build a rigid 15 pound speaker. Open baffle speakers don't have internal pressurization to cause problems so a 60-70 pound floor standing example can be free of cabinet coloration (I did that with Siegfried's Orion design).
>How much are you paying for the cabinet versus the drivers on an expensive pair of speakers?
Depends on construction technique, labor costs, finish. Many large vendors speakers are cut on CNC routers and assembled with miter fold construction. MDF is nearly free, common hardwood veneers are cheap and don't take much to apply to the whole sheet in a veneer press, semi-skilled Chinese workers make a lot of speakers for $150 a month in wages, and the drivers should be more; but most of the price is overhead in terms of advertising costs, dealer profits, dealer overhead, etc.
American labor is pricey. Craftsmen are more expensive than factory workers. Use the Orion+ built by Don Naples at Wood Artistry as an example. You start at around $6800 less $1900 for drivers in small quantities, $500 for cross-over parts, $300 for cross-over labor, $170 in licensing costs, and are left with cabinet costs of $3700 of which maybe $3500 is labor and a screaming deal (California is not cheap).
Larger companies get better deals on drivers (quantity) and labor (factory workers not craftsman) but some really cut corners on drivers. $15-$25K a pair covering advertising, overhead, markups through the distribution chain, maybe amortized engineering costs, etc. is not out of line.