= Solution
Approximating the skin as a uniform thin water shell with density $1000\,\mathrm{kg\,m^{-3}}$,
$$
\boxed{m_{\rm skin}\simeq4\pi r^2\tau\rho_w=1.26\times10^{-4}\,\mathrm{kg}=0.126\,\mathrm g.}
$$
This is about \b[2500 times] the $5.03\times10^{-8}\,\mathrm{kg}$ buoyant mass of the enclosed <gas>. The film weight therefore dominates the bubble's downward gravitational <force> under the stated assumptions. Equal-temperature air inside does not provide a net lift to balance it: an apparently floating bubble can be transiently supported by air currents or have different internal temperature/composition. Film thickness is generally nonuniform and changes with drainage and evaporation; the uniform $1\,\mu\mathrm m$ thickness is an estimate, not a stable equilibrium condition.
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