World weather is really an oxymoron, that is, two words together that contradict.
Weather is what happens locally over short time periods.
It rains, is frosty, snows or the wind blows according to patterns in the movement of air masses in the lower atmosphere. And although air masses can be large, such as the high pressure cells that sit across the continent of Australia for days at a time, they mostly fluctuate and move in ways that result in local weather.
So it is not possible to have global weather.
Perhaps what is meant is the individual weather patterns that affect each and every part of the world, gathered into something larger.
Although for this climate is a more precise term.
Perhaps where we see weather patterns changing we believe they are influenced by global phenomenon and we extend the concept to everywhere.
Confusion of terms is something that happens often in science.
Jargon is created and, by definition, used by only a few specialists. The words created are then easily misunderstood and misplaced by those not in the loop.
Global weather is more likely a term that is a simplification to try and link climate with the weather.
Only this simplification becomes misleading because it is climate that changes, not the weather.