  We update earlier lattice results for the binding energies of the flavor
antitriplet of strong-interaction-stable doubly bottom, $J^P=1^+$ tetraquarks,
employing an extended sink construction which produces significantly improved
ground-state effective-mass plateaus, as well as new, larger-volume ensembles
which reduce possible finite-volume effects at lighter pion masses. The updated
bindings are $115(17)$ MeV for the $I=0$ member of the antitriplet and $47(8)$
MeV for its $I=1/2$ partner. We also provide an update of our earlier study of
the variable heavy mass dependence of binding in the $1^+$ channel and new
results on this dependence for binding in the $0^+$ channel, accessible when
the two heavy quarks have unequal masses. Implications of these results of
potential relevance to experimental searches for signals of the production of
doubly bottom tetraquarks and/or a possible bottom-charm partner of the
$T_{cc}$ are also discussed.
