Magnetic resonance imaging (MRI) has garnered significant attention due to its non-ionizing radiation, non-invasive imaging capabilities, and superior soft tissue contrast. Compared to high-field systems, ultra-low field (ULF) MRI boasts advantages such as low cost and high portability. It is highly sensitive to local field change sensed by protons, which are reflected in the relaxation times, such as the spin-spin relaxation time (T₂). This sensitivity enables precise discrimination of distinct relaxation components. In this study, seven phantoms were prepared with controlled peanut oil mass fractions (0%, 5%, 10%, 20%, 30%, 40%, and 50% w/w). The phantoms were placed in an ULF MRI system and continuous spin echo trains were acquired by the Carr-Purcell-Meiboom-Gill (CPMG) pulse sequence. By performing inverse Laplace transform, T2 time-domain spectra of these echo trains were derived. We found a consistent correlation between the peak positions (T21) of short relaxation components, the areas (S21) under these peaks, and fat content in peanut oil phantom. Based on this correlation, a linear regression model was developed to predict peanut oil mass fractions based on T₂ relaxation characteristics. The fat contents in the phantoms evaluated by the linear regression model were verified through the Soxhlet extraction method. This research provides a robust methodology for future investigation into non-invasive in vivo fat quantification based on an ULF MRI system.