Shooter,
Anything is possible, but I doubt it is practical for a small merchant. I'm making the leap of faith that you don't have the volume to justify much in the way of custom integrations.
From a purely logistical point of view, if you've got a little volume its easy enough to negotiate a discount off an LTL (Less-Than-Truckload) Carrier's filed tarriffs. Then it is simply a matter of doing a lookup within their rate table for a given class of materials, deducting your discount, multiplying by weight (and in rare instance DIM) and then adding any/all applicable accessorial charges (fuel surcharges, dunning, etc.) to get the true rate.
Large customers get this load rating via real-time feed. However, I don't know of

offering to integrate LTL / TL carrier real-time feeds and as I said you probably don't have the volume to justify paying to integrate it yourself via a

custom shipping mode.
I hope I'm wrong, but that would be my guess.
Ed