Most fret buzzing is a result of the vibrating string contacting another fret as it vibrates in an oscillating arc. There are several things that commonly cause this to happen.
Neck does not have enough relief or has a back bow. The vibrating/oscillating string must clear all the frets between where it is fretted and the bridge. If the neck is perfectly straight or back bowed, the string is likely to contact one of the frets between the fret you are pressing it against and the bridge. To correct this, tighten the truss rod until there is a slight relief in the neck to provide more clearance on the downstream frets when you fret a note.
To check the amount of relief, you can use one finger to press the string down against the first fret and another to press against one of the frets near where the neck joins the body and see how much clearance you have above the frets in between these two points. If the string is touching any of the frets between the two you are holding it down on, you do not have sufficient relief. Pressing the string against frets on opposing ends of the fretboard, takes your bridge height adjustment out of the equation for this test.
Even if the strings are not touching any frets in this test, you still may not have enough relief if they are too close to one or more frets. The string oscillates in an arc when you play it. The harder you pick the string, the wider the arc. Also, different gauge strings will have different oscillation patterns due to the tension required to bring them in tune. Less tension generally means a wider oscillation arc and therefore more relief is needed.
Check the relief on both the bass and treble side of the neck. if there is relief on one side and a back bow on the other, that is a sign of a twisted neck and a serious problem.
If the relief is sufficient, try adjusting the bridge height. Your guitar is likely to have a bridge height adjustment for each string. You mentioned in your question that you have made this adjustment. Try it again after you are sure you have enough relief after truss rod adjustment.
Another less common but potential area where strings can end up too close to the frets is in the nut. Smaller diameter strings may sit farther down in the slot and the slot can deepen with wear and cause the strings to sit closer to the fret. Nuts are not generally adjustably (temporary fixes with super glue notwithstanding) so if your nut slots become worn too deep, you will need to replace the nut.
Another common cause of fret buzz - is groves in some frets. Steel strings against nickle frets will eventually cut grooves in the frets where the strings contact the frets. This happens primarily on the unwound plain steel strings. Also, bending strings when playing solos can act like a file and file the frets down so they lose height relative to the other frets. If you get a buzz when playing notes on certain frets, check to see if that fret is worn or grooved under the offending string. You can see the condition of the frets more easily if you use a magnifying glass.
One other thing than can cause fret buzz - is one or more frets may be too high, relative to the other frets. This can happen if the fret works itself loose in the fret slot or was not seated correctly when installed.
You can check for high or uneven frets with a straightedge such as a ruler. You need a straightedge long enough to cover at least 5 or more frets at a time - but not too long. Place the straightedge against the frets at various places on the fretboard and on various frets. The straightedge should evenly contact at least 5 frets at a time without rocking or see sawing. As you slide the straightedge from the nut towards the body, if you encounter a fret that acts like a fulcrum and allows you to rock the straightedge from lower frets to higher frets like a see saw, then you have found a high fret which may need to be repaired.
Repairing a high fret may mean properly seating it in the groove on the fretboard by tapping it in (with the neck properly braced and possibly heating just the fret to soften any glue), and/or filing it with the correct size fret file and crowning it with the proper tool. This type repair should be made by a professional.
If some of the frets are grooved or worn more than others, or if several frets are too high, it might be time for a fret job. If uneven height frets are the main problem - a qualified luthier or guitar repair technician, using the proper fret files and fret levels, can file all the frets down and crown and level them so that all buzzing is eliminated. Many well played guitars will need a fret job at some point in time and perhaps regularly (if played often enough).
Hopefully you will be able to determine the cause of your fret buzzing, and if it's any of the things mentioned above (besides an unlikely twisted neck) you should be able to solve the problem.