  We combined deep U-band imaging from the KPNO-4m/MOSAIC camera with very deep
multi-waveband data from the optical to infrared, to select Lyman Break
Galaxies (LBGs) at z~3 using U-V and V-R colors in the Subaru Deep Field. With
the resulting sample of 5161 LBGs, we construct the UV luminosity function down
to $M_{UV} = -18$ and find a steep faint-end slope of $\alpha=-1.78 \pm 0.05$.
We analyze rest-frame UV-to-IR spectral energy distributions generated from the
median optical photometry and photometry on median-stacked IR images. In the
stacks of faint LBGs, we find a background depression centered on the galaxy.
This deficit results from the systematic difficulty of SExtractor in finding
faint galaxies in regions with higher-than-average surface densities of
foreground galaxies. We corrected our stacked magnitudes for this. Best-fit
stellar population templates for the stacked LBG SEDs indicate stellar masses
and star-formation rates of log M*/Msun = 10 and 50 M$_\odot$/yr at i' = 24,
down to log M*/Msun = 8 and = 3 M$_\odot$/yr at i' = 27. For the faint stacked
LBGs there is a 1-mag excess over the expected stellar continuum in the K-band,
which we attribute to redshifted [OIII]4959+5007 and H$\beta$ lines. Their
implied equivalent widths increase with decreasing mass, reaching $\rm{EW_0([O
III]4959,5007+H\beta)}$ =1500A in the faintest bin. Such strong [OIII] emission
is seen only in a miniscule fraction of the most extreme local emission-line
galaxies, but it probably universal in the faint galaxies that reionized the
universe. Finally, we analyze clustering by computing the angular correlation
function and performing halo occupation distribution (HOD) analysis. We find a
mean dark halo mass of log(Mhalo/h) Msun = 11.29$\pm 0.12$ for the full sample
of LBGs, and log(Mhalo/h) Msun = 11.49$\pm 0.1$ for the brightest half.
