What does “background evidence” mean?

Background evidence is information that helps establish the general historical setting but does not directly establish your central proposition.

Example:

“Britain had many small businesses during industrialization.”

That could provide background about the capitalist economy.

But it does not demonstrate:

“Former serfs who became workers subsequently entered the middle class.”

What does “at best” mean?

At best means:

“Even under the most favorable interpretation, this is the greatest usefulness that this evidence could have.”

So when I said:

“background evidence at best,”

I meant:

“Even if we tried to make this evidence useful, it would only establish general context, not your central causal proposition.”

But after your clarification, I would go further:

For your particular section, you do not need to include that evidence at all.

What is central evidence?

Central evidence directly bears upon the proposition you are trying to establish.

For your argument:

Evidence that formerly enslaved people entered wage labour

is central.

Evidence that some formerly enslaved workers accumulated economic resources or established businesses

is central to your next step.

Evidence about unrelated merchants who were already middle class

is not central.

So yes—you were right to reject my Barker discussion as irrelevant to this particular argument.