  We make use of sensitive (9.3 microJy/beam RMS) 1.2mm-continuum observations
from the ASPECS ALMA large program of the Hubble Ultra Deep Field (HUDF) to
probe dust-enshrouded star formation from 1362 Lyman-break galaxies spanning
the redshift range z=1.5-10 (to ~7-28 Msolar/yr at 4 sigma over the entire
range). We find that the fraction of ALMA-detected galaxies in our z=1.5-10
samples increases steeply with stellar mass, with the detection fraction rising
from 0% at 10^9 Msolar to 85(-18)(+9)% at >10^{10} Msolar. Moreover, stacking
all 1253 low-mass (<10^{9.25} Msolar) galaxies over the ASPECS footprint, we
find a mean continuum flux of -0.1+/-0.4 microJy/beam, implying a hard upper
limit on the obscured SFR of <0.6 Msolar/yr (4 sigma) in a typical low-mass
galaxy. The correlation between the infrared excess IRX of UV-selected galaxies
(L(IR)/L(UV)) and the UV-continuum slope is also seen in our ASPECS data and
shows consistency with a Calzetti-like relation at >10^{9.5} M_{solar} and a
SMC-like relation at lower masses. Using stellar-mass and beta measurements for
z~2 galaxies over CANDELS, we derive a new empirical relation between beta and
stellar mass and then use this correlation to show that our IRX-beta and
IRX-stellar mass relations are consistent with each other. We then use these
constraints to express the infrared excess as a bivariate function of beta and
stellar mass. Finally, we present updated estimates of star-formation rate
density determinations at z>3, leveraging current improvements in the measured
infrared excess and recent probes of ultra-luminous far-IR galaxies at z>2.
