Layer specific functional MRI requires high spatial resolution data. An approach often used for compensating for the poor signal to noise ratio (SNR) associated with small voxel sizes consists of integrating the signal from voxels at a given cortical depth over a patch of cortex. After this integration, physiological noise is expected to be the dominant noise source in the signal. In this context, the sensitivity gain in moving to higher static field strengths is expected to be lower than when thermal noise dominates. In this work, activation profiles in response to the same visual stimulus are compared at 1.5 T, 3 T and 7 T using a multi-echo, gradient echo (GE) FLASH sequence, with a 0.75 mm isotropic voxel size and the cortical integration approach. The results show that after integrating over a patch of cortex between 40 and 100 mm3(at 7 T and 1.5 T, respectively), the signal is in the physiological noise dominated regime, and that the obtained activation profiles are similar at the three different field strengths for equivalent echo times. The evolution of the resting-state signal over echo time indicates that BOLD-like noise is the dominant source of physiological noise. Consequently, the functional contrast to noise ratio is not strongly echo-time or field-strength dependent. The results show that compared to 7T, the gold standard, laminar GE-BOLD fMRI at lower field strengths is feasible at the cost of poorer spatial resolution (larger cortical integration extensions) and lower efficiency.