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I have a 1291 BBb 4v that I'm intending to post for sale after Christmas.
I bought it this year (July, I think) with MTS hard case.
Valves have been vented, springs replaced with Yamaha euphonium springs.

It's a joy to play, but more horn than I can justify owning (euphonium player doubling on tuba for church).

If you are looking to downsize in BBb, consider the MW Hojo. There are several comments/reviews on this site. It may be too small in bore size for you but would be lighter and easier to schelp. I am having the same trouble. I am going to try an Olds O-99 for a while and see how it works. The horn that is really too heavy for me now is the 4v version of the VMI 3302, the 3301. The 3302 would be even slightly heavier. I believe they will weigh about the same as the 1291, not as heavy as the Conn, but too heavy for me. You might be able to get respective weights from posters. I can get the 3301 weight for you if you like. BTW, I absolute love to play the 3301. Excellent pitch. Wonderful sound, not too woofy and not to direct. The response is astounding. If it weighed 6 or 7 pounds less, I would be set for life.

Well, the 3302 and the 1291 both weigh about the same. The biggest difference is in the bore size, with the beath saving edge going to the 3302 because of the smaller bore. Sound quality I would give the nod to the Miraphone 1291 as it is un-surpassed in the sound and playability part of the deal. I personally own the 5 valve 1291 BBb tuba and love it. Yes, I'm getting a bit on in years and use a C4 or TU23 moutrhpiece on it to make it more air efficient, but it also gives the sound a little more "front" to the attack and a little more clarity in the articulation - both of which I like for Brass Band work. Sometimes I will use a Rose Solo Miraphone mouthpiece on it for a tad more depth.

The 3302 is a nice horn. Very playable with a decent low register. I find that tthe Miraphone low register is more open and resonant (bigger cave) and a little easier to play as you get lower.

Since all BBb tubas are the same length, the only way to cut back on the weight is to go to a thinner metal, like in the Cerveny, or to a smaller bell like on the 282 BBb Miraphone. Other than that you have X amount of tubing and there's not a lot you can do about it.

The 1291 BBb and the New Yorker are about the same size - both fit in the same gig bag. Personally, as you can tell, my preference runs toward the 1291BBb. The biggest reason is what gene Pokorny refers to as the "Sonic Depth Charge". This horn can do it, and do it extremely well. I've made a few minor improvements in the inhalation process and tweaked the mouthpiece a bit to get it so that it is better on the air usage. It is such a resonant horn that you don't need to play it hard to get it to do what other horns need. There appears to be an ample amount of "wattage' built into the horn. It also helps to have a reasonably efficient embouchure to keep things under control.

Let me know if you have more questions. I may be able to help.

The best wishes to all for the holiday season.
Roger