  We perform modeling investigations to aid in understanding the atmospheres
and composition of small planets of ~2-4 Earth radii, which are now known to be
common in our galaxy. GJ 1214b is a well studied example whose atmospheric
transmission spectrum has been observed by many investigators. Here we take a
step back from GJ 1214b to investigate the role that planetary mass,
composition, and temperature play in impacting the transmission spectra of
these low-mass low-density (LMLD) planets. Under the assumption that these
planets accrete modest hydrogen-dominated atmospheres and planetesimals, we use
population synthesis models to show that predicted metal enrichments of the
H/He envelope are high, with metal mass fraction Z_env values commonly 0.6 to
0.9, or ~100 to 400+ times solar. The high mean molecular weight of such
atmospheres (\mu ~ 5-12) would naturally help to flatten the transmission
spectrum of most LMLD planets. The high metal abundance would also provide
significant condensible material for cloud formation. It is known that the H/He
abundance in Uranus and Neptune decreases with depth, and we show that
atmospheric evaporation of LMLD planets could expose atmospheric layers with
gradually higher Z_env. However, values of Z_env close to solar composition can
also arise, so diversity should be expected. Photochemically produced hazes,
potentially due to methane photolysis, are another possibility for obscuring
transmission spectra. Such hazes may not form above T_eq of ~800-1100 K, which
is testable if such warm, otherwise low mean molecular weight atmospheres are
stable against atmospheric evaporation. We find that available transmission
data are consistent with relatively high mean molecular weight atmospheres for
GJ 1214b and "warm Neptune" GJ 436b. We examine future prospects for
characterizing GJ 1214b with Hubble and the James Webb Space Telescope.
