We present a characterization of the physical properties of a sample of 35 securely detected, dusty galaxies in the deep ALMA 1.2 mm image obtained as part of the ALMA Spectroscopic Survey in the Hubble Ultra Deep Field (ASPECS) Large Program. This sample is complemented by 26 additional sources identified via an optical/infrared source positional prior. Using their well-characterized spectral energy distributions, we derive median stellar masses and star formation rates (SFR) of 4.8 × 1010, M⊙ and 30 M yr-1, respectively, and interquartile ranges of (2.4-11.7) × 1010 M and 20-50 M yr-1. We derive a median spectroscopic redshift of 1.8 with an interquartile range 1.1-2.6, significantly lower than submillimeter galaxies detected in shallower, wide-field surveys. We find that 59% ± 13%, 6% ± 4%, and 34% ± 9% of our sources are within, above, and below±0.4 dex from the SFR-stellar-mass relation or main sequence (MS), respectively. The ASPECS galaxies closely follow the SFR-molecular gas mass relation and other previously established scaling relations, confirming a factor of five increase of the gas-to-stellar-mass ratio from z = 0.5 to 2.5 and a mild evolution of the gas depletion timescales with a typical value of 0.7 Gyr at z = 1-3. ASPECS galaxies located significantly below the MS, a poorly exploited parameter space, have low gas-to-stellar-mass ratios of ∼0.1-0.2 and long depletion timescales >1 Gyr. Galaxies along the MS dominate the cosmic density of molecular gas at all redshifts. Systems above the MS have an increasing contribution to the total gas reservoirs from z < 1 to z = 2.5, while the opposite is found for galaxies below the MS.