  We report on the timing observations of the millisecond pulsar PSR J2055+3829
originally discovered as part of the SPAN512 survey conducted with the
Nan\c{c}ay Radio Telescope. The pulsar has a rotational period of 2.089 ms, and
is in a tight 3.1 hr orbit around a very low mass ($0.023 \leq m_c \lesssim
0.053$ M$_\odot$, 90\% c.l.) companion. Our 1.4 GHz observations reveal the
presence of eclipses of the pulsar's radio signal caused by the outflow of
material from the companion, for a few minutes around superior conjunction of
the pulsar. The very low companion mass, the observation of radio eclipses, and
the detection of time variations of the orbital period establish PSR J2055+3829
as a `black widow' (BW) pulsar. Inspection of the radio signal from the pulsar
during ingress and egress phases shows that the eclipses in PSR J2055+3829 are
asymmetric and variable, as is commonly observed in other similar systems. More
generally, the orbital properties of the new pulsar are found to be very
similar to those of other known eclipsing BW pulsars. No gamma-ray source is
detected at the location of the pulsar in recent \textit{Fermi}-LAT source
catalogs. We used the timing ephemeris to search ten years of \textit{Fermi}
Large Area Telescope (LAT) data for gamma-ray pulsations, but were unable to
detect any, possibly because of the pulsar's large distance. We finally
compared the mass functions of eclipsing and non-eclipsing BW pulsars and
confirmed previous findings that eclipsing BWs have higher mass functions than
their non-eclipsing counterparts. Larger inclinations could explain the higher
mass functions of eclipsing BWs. On the other hand, the mass function
distributions of Galactic disk and globular cluster BWs appear to be
consistent, suggesting, despite the very different environments, the existence
of common mechanisms taking place in the last stages of evolution of BWs.
