I have ridden at weights from 300 - 365 and have found that higher volume tires are better than a shock.

I don't have a bad back, so I can't say for sure how it will work for you, but going with large volume tires at near max pressure provides good comfort for me.

Going with as low a pressure as you can without pinch flats helps the comfort level too.

I haven't ridden a fat bike, but the few people I have talked to that ride them, they say they are wonderful for rough terrain, but even at relatively high tire pressure (for a fat bike tire) they are pretty sluggish on pavement or smooth trails.