I think the back pain issue is going to vary primarily as a matter of proportion, not necessarily size. As many others have pointed out, 38DDs on Godzilla are not going to be same as 38DDs on a 5’5" 135lb female (and I’m not talking about the scales and green color variation).
Speaking from personal experience, prior to my breast reduction (which I highly, highly advise to anybody in a similar situation to get one if you can) I hovered around a 40G at 21. I’m 5’8", and have always had a curvy, medium-large figure, though just up to the surgery I was bordering on plus sizes (primarily because my boobs were so huge I couldn’t exercise–back pain, shoulder pain from the bra straps, putting an eye out, the previously mentioned underboob rash, the hassle of having to wear two or three bras [one to contain, one to lift, and one to smooth everything else so it didn’t look like I had quadraboobs]plus all the people staring). Even with the extra baggage I wound up carrying because of them, my boobs were way too big for my body. The back pain wasn’t excruciating, but it was nearly constant, though sometimes way worse than others. Even the best-fitting properly-sized bras also caused some pain in terms of the straps cutting in to my shoulders, the under-wires poking out, etc. (And I hear you guys on having to shell out 3xs as much for a hideous bra that only lasts a quarter of the time before it warps). I tried weight-lifting, yoga, the whole bit, but the help was minimal to non-existent, and I figured the back pain was only going to get worse as I got older.
A year after the surgery, (which it took 3 years before I could convince health care to cover) I’m still what a lot of you would consider extremely big-breasted, but I don’t, considering where I was. (I’m in the 38DD-range, but it’s going down a little as I continue to lose weight). I’d like it if they were a little smaller, but am so much happier and healthier with them as they are now. Exercize is not some horrific undertaking, and the back pain/bra strap rut issue is completely gone. Being able to fit into normal clothes, get the tops and bottoms to swimsuits in the same place–and have the top in stock–is also amazing. The amount of time and level of pain I’d experience in terms of just the boobs themselves hurting is identical (other than the two weeks post op) to what it was before, with only minimal pain with my period from time to time.
So to answer the OP, I’d say having EXTREMELY super large breasts almost always causes back pain. Having pretty big breasts (when taking into consideration the size of the person they’re on) doesn’t, necessarily. It’s a matter of how big we’re talking about.