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Atomic accelerometers and gravimeters are usually based on freely falling atoms in atomic fountains, which not only limits their size but also their robustness to environmental factors, such as tilts, magnetic fields, and vibrations. Such limitations have precluded their broad adoption in the field, for geophysics, geology, and inertial navigation. More recently, atom interferometers based on holding atoms in an optical lattice have been developed. Such gravimeters also suppress the influence of vibrations in the frequency range of ∼1 Hz and above by several orders of magnitude relative to conventional atomic gravimeters. Here, we show that such interferometers are robust to tilts of more than 8 mrad with respect to the vertical and can suppress the effect of even strong environmental magnetic fields and field gradients by using atoms in the F=3, 4 hyperfine ground states as co-magnetometers, potentially eliminating the need for shielding. We demonstrate gravimeter sensitivity of 0.7 mGal/Hz (1 mGal = 10 μm/s2) in a compact geometry where atoms only travel over millimeters of space.