One of the most common enigmas in saxophone physics: the bigger the horn, the more difficult it is to produce a clear well-rounded tone in the higher octave register. Are you having this issue with all the notes in the higher octave, or just some of them? Better quality Bari saxes & mouthpieces will usually allow a cleaner tone, but you need to check these three things:
1) Your Embouchure & Breathing: If you are not used to playing such a large horn, it is like everything else. Only time practicing & playing the horn will condition you to play it. The Bari sax is going to require you to open your throat and abdomenal cavity more and exchange more air as you regularly blow the horn.
2) The Mouthpiece/Reed Combination: Much of the time the stock mouthpiece that comes with the horn (depending on the brand) may not have a facing that is large enough for you, or you may be using too soft a reed. If your mouthpiece has a #2 facing and you're using #2 reeds, you might try (least expensive) using a thicker reed or (more expensive) investing in your own personal Bari mouthpiece with a facing & reed combination you are comfortable with.
3) [THE MOST LIKELY CULPRIT] Problems w/ Keys Sealing (leaks) or Opening: The pads on the keys become unseated or get out-of-align OR the cork or felt gets wore-down on the key mechanisms. Even more critical are those keys at the top of the horn that open/close to control your "octave" registers. A Bari sax is a bigger horn w/ bigger keys that has normally been used a lot by many others (as most Bari's are). If it is a school horn, then it has been subjected to being knocked-around, outside weather, humidity from playing & spit, etc.
Check the two "octave" keys first (at the top of the body of the horn) to make sure they are closing properly and/or opening up fully. If they are not, check the "cork" (first) on all the octave key mechanisms as well as checking the key pads; they may need to be replaced.
Do the same thing with the left-hand & right-hand high-register keys. Then move on down to those keys operated by your left hand (B/A/G/G#) and check them as well. Notice...we started at the top of the horn and work our way down.
If uncomfortable with this process, I recommend having the horn taken to a reputable saxophone repair shop in your area to be checked. I don't claim to be the expert; I'm just relaying info handed-down from former sax teachers and from bitter experience. Hope some of this helps....