How could emancipation weaken the Confederacy if the Confederacy rejected it?

This is an important distinction.

The Emancipation Proclamation did not simply become Confederate law.

It applied to enslaved people in areas designated as being in rebellion and depended on Union military power for implementation.

But it could nevertheless weaken the Confederacy through its effects, rather than because Confederate authorities accepted the proclamation.

For example:

1. Flight of enslaved people

As Union armies entered Confederate territory, enslaved people could escape to Union lines.

That deprived Confederate plantations of labor.

2. Union recruitment

Emancipation helped open the way for Black men to enter the Union military.

This increased Union manpower while weakening the Confederate labor system.

3. Labor disruption

Confederate agriculture depended heavily upon enslaved labor.

When enslaved workers escaped or were liberated in Union-controlled areas, Confederate production could suffer.

4. Political effect

Emancipation changed the war's political meaning:

The Union was increasingly fighting not merely to restore the Union but also against slavery.

This made foreign recognition of the Confederacy more difficult and strengthened the Union's moral and diplomatic position.

So the correct formulation is not:

“The Confederacy accepted emancipation and therefore its system weakened.”

Rather:

Union emancipation policy, combined with military advance, disrupted the Confederate system of enslaved labor and contributed to weakening its economic and military capacity.