The largest usable tuba that I have played/worked on is the Rudolf Meinl 6/4 BBb, a truly huge instrument that is well-proportioned, featuring a 22" diameter bell rim and an approx. .870" valve bore. I also measured the main tuning slide which had respective bores of .970" incoming and approx. 1.1" on the large side. The top bow of this instrument is similar in size to the bottom bow of an Alex 163.
Initially, it is a little like holding a filing cabinet, but I was surprised to find that after about 20 minutes, it started feeling normal to me.