Can too many layers of shingles cause sagging?

Weight contributes, and most codes limit the number of layers partly for that reason. More often the layers are a symptom: a roof that was covered over twice rather than stripped is a roof whose deck has not been inspected in decades.

Answers · Is something wrong?

My roof looks like it is sagging. What does that mean?

The short answer

Treat it as structural until someone qualified says otherwise. Common causes are a deteriorated deck from long-term moisture, undersized or damaged framing, too many layers of roofing, or a load the structure was not designed for. A roofer can identify it; a structural engineer is the one who specifies the repair.

What to establish

Whether it is new. Old houses settle and many have had a gentle wave in the ridge for decades. A dip that has appeared or deepened is different.
Where it is. A dip between rafters is decking; a dip along the ridge is framing; a dip at one end can be a wall or foundation problem showing up at the top.
Whether there is water history in the attic below it.
How many layers of roofing are on it.

Why it is not only a roofing question

Roof structure carries load, and a repair that restores the surface without addressing why the structure moved is cosmetic. Where the cause is framing, an engineer's specification protects you twice: it makes the repair correct, and it gives you a document if the work is ever questioned at sale.

Also asked

Can too many layers of shingles cause sagging?: Weight contributes, and most codes limit the number of layers partly for that reason. More often the layers are a symptom: a roof that was covered over twice rather than stripped is a roof whose deck has not been inspected in decades.

General information about roofs and about hiring, not advice about your building. Roofing contractor licensing, permits, insurance practice and deductible rules are set state by state and province by province across the United States and Canada, so your own authority is the current answer.