  The GLAST-AGILE Support Program (GASP) of the Whole Earth Blazar Telescope
(WEBT) monitored BL Lacertae in 2008-2009 at radio, near-IR, and optical
frequencies. During this period, high-energy observations were performed by
XMM-Newton, Swift, and Fermi. We analyse these data with particular attention
to the calibration of Swift UV data, and apply a helical jet model to interpret
the source broad-band variability. The GASP-WEBT observations show an optical
flare in 2008 February-March, and oscillations of several tenths of mag on a
few-day time scale afterwards. The radio flux is only mildly variable. The UV
data from both XMM-Newton and Swift seem to confirm a UV excess that is likely
caused by thermal emission from the accretion disc. The X-ray data from
XMM-Newton indicate a strongly concave spectrum, as well as moderate flux
variability on an hour time scale. The Swift X-ray data reveal fast (interday)
flux changes, not correlated with those observed at lower energies. We compare
the spectral energy distribution (SED) corresponding to the 2008 low-brightness
state, which was characterised by a synchrotron dominance, to the 1997 outburst
state, where the inverse-Compton emission was prevailing. A fit with an
inhomogeneous helical jet model suggests that two synchrotron components are at
work with their self inverse-Compton emission. Most likely, they represent the
radiation from two distinct emitting regions in the jet. We show that the
difference between the source SEDs in 2008 and 1997 can be explained in terms
of pure geometrical variations. The outburst state occurred when the
jet-emitting regions were better aligned with the line of sight, producing an
increase of the Doppler beaming factor. Our analysis demonstrates that the jet
geometry can play an extremely important role in the BL Lacertae flux and
spectral variability.
