I can only guess, but I will ...
tl;dr synopsis: it's because of the extra stuff in the 125SE to cover lots of different impedances make the core and coil bigger.
Transformer weight generally is representative of low frequency response if everything else is equal. For E-I cores, the proportions are fixed, and the amount of magnetic field energy that can be stored in there is dependent on the core area, which directly relates to weight. That is truest when the transformer is wound nearly perfectly, with coil wires neatly and completely filling the winding window, in a non-gapped core.
SE output transformers have to be gapped in general; they're a form of a pre-loaded inductor where the inductor is kept at a field density halfway to saturation. In a gapped inductor (and transformer), the magnetic field is mostly in the gap. The iron is merely a quick and easy path for the field to get around to the other end of the gap. The inductance is much smaller because of the gap, so they're larger and heavier than a push-pull transformer of the same power output.
The gap-induced reduction in primary inductance means that for an audio transformer at a specified primary impedance, you need a lot more iron and primary turns to get the primary inductance back up. It gets heavier. But iron isn't the only factor there. For a multi-impedance primary, you have to put in enough turns of copper to get the primary inductance high enough for the highest primary impedance you would see. This means more turns, or much more of the wire area wasted in tapping the primary and bringing out leads for the taps. Hammond usually specifies "worst case" situations for their transfomers, so I'd guess that they specified the worst case for frequency response in terms of the primary tap used. Getting to that spec point, the designer probably used more iron and copper to cover all the cases.
I think...
"It's not what we don't know that gets us in trouble. It's what we know for sure that just ain't so"
Mark Twain
