I have a Bro-Tek bolt-on thumb on my 2310 which I use for holding logs up for cutting. The BH can definitely lift a lot of weight, to the point that you'd better make sure the stabilizer feet are down or it can easily tip the tractor over.
On the occasion where I have a log that's too heavy to hold up with the BH, I use the FEL to lift it a bit and put a small log section under the larger log to get it off the ground for cutting. Eventually, it'll get light enough that the BH/thumb can lift it.
One other thing I like about the BH/thumb combo is that I can swing the BH left/right to pull logs out after I've cut some off.
But yes, there's definitely a limit to what a SCUT or CUT can lift. (Hey-- if the logs get that big, call in the pros!)