Abdominal PET-MR scans commonly combine free-breathing PET with breathhold or respiratory-triggered MR scans (T1/T2-weighted). This ensures high MR image quality but can lead to PET images impaired by motion blurring. Furthermore, PET can suffer from artefacts close to tissue-lung interfaces due to misalignment of breathhold MR-based attenuation correction (AC) information used for free-breathing PET. Here we present a free-breathing MR-technique which yields motion-compensated 3D T1-weighted and T2-weighted MR images. Respiratory-resolved AC maps and motion compensation improved uptake values (125±131%) and resolution (22±16%). Respiratory motion information is obtained with an accuracy of 1.3±0.1mm without an increase in scan time.