COMMA + Verb-ing Modifier Confusion [DOER of action must make sense]

Often (though not always), there is a 'cause effect' relationship with comma,--ing modifiers.

So it's not that weather 'does' something, it's that 'weather being cold' causes something (slower sales).

"...weather, which was colder and wetter than usual, slowing sales of barbecue grills and lawn furniture"

can be thought of as:

"...weather, which was colder and wetter than usual, [and therefore slowed] sales of barbecue grills and lawn furniture."

Why did sales of BBQ grills and lawn furniture slow? Because the weather was colder and wetter than usual.

The cause effect can also be reversed:

"The sword and shield were considered essential for warriors, protecting a soldier and allowing him to fight the enemy at the same time."

Can be thought of as:

"The sword and shield were considered essential for warriors [because they protected] a soldier and [because they allowed] him to fight the enemy at the same time."

Why were they considered essential? Because they protected a solider and allowed a soldier to fight the enemy.

The other way to thin about comma,--ing is to think of them as 'while' modifiers.

"We walked down the street, whistling a song."

Means "While he walked down the street, he whistled a song." (or, I suppose, While he whistled a song, he walked down the street." Either works).