  We investigate the properties of the galaxies selected from the deepest
850-micron survey undertaken to date with SCUBA-2 on the JCMT. This deep
850-micron imaging was taken in parallel with deep 450-micron imaging in the
very best observing conditions as part of the SCUBA-2 Cosmology Legacy Survey.
A total of 106 sources were uncovered at 850 microns from ~150, sq. arcmin in
the centre of the COSMOS/UltraVISTA/CANDELS field, imaged to a typical rms
depth of ~0.25 mJy. We utilise the wealth of available deep multi-frequency
data to establish the complete redshift distribution for this sample, yielding
<z> = 2.38 +- 0.09, a mean redshift comparable with that derived for all but
the brightest previous sub-mm samples. We have also been able to establish the
stellar masses of the majority of the galaxy identifications, enabling us to
explore their location on the star-formation-rate:stellar-mass (SFR:M*) plane.
Crucially, our new deep sample reaches flux densities equivalent to SFR ~ 100
Msun/yr, enabling us to confirm that sub-mm galaxies form the high-mass end of
the `main sequence' (MS) of star-forming galaxies at z > 1.5 (with a mean
specific SFR of sSFR = 2.25 +- 0.19 /Gyr at z ~ 2.5). Our results are
consistent with no significant flattening of the MS towards high masses at
these redshifts, suggesting that reports of such flattening possibly arise from
under-estimates of dust-enshrouded star-formation activity in massive
star-forming galaxies. However, our findings add to the growing evidence that
average sSFR rises only slowly at high redshift, resulting in log(sSFR) being
an apparently simple linear function of the age of the Universe.
