Which invaders attacked the roman empire's territory and caused it to weaken?

Germanic tribes -- especially the Visigoths -- attacked the Roman empire and caused it to weaken.

There had been ongoing migration of Germanic tribes into Roman empire territory, that had a gradual weakening effect on the empire.  The western tribes consisted of groups such as the Alamanni, Franks, Angles, and Saxons.  There was also a large group of Germanic tribes known as the Goths.  We speak of the Visigoths and Ostrogoths do distinguish between the western and eastern Goths.  The Visigoths (western Goths) invaded the Roman Empire, and defeated Roman armies at the Battle of Adrianople in 378.  Later, the Visigoths even invaded Italy and sacked the city of Rome in 410.  So I suspect the answer your question is primarily looking for is the Visigoths.