= Solution
An inverse-square field spreads through area proportional to squared distance. More generally the <flux> contribution of a point source is proportional to the <solid angle> subtended by a surface element; the oriented <solid angles> sum to $4\pi$ for an enclosed source and zero for an exterior one. <Superposition> extends this to a <mass distribution>.
<Newton's law of universal gravitation> gives $\mathbf g=-GM\hat{\mathbf r}/r^2$ for a <point mass>. A surrounding sphere therefore has <flux> $-4\pi GM$, so
$$
\boxed{C=4\pi G,\qquad \oint\mathbf g\cdot d\mathbf S=-4\pi GM_{\rm enc}.}
$$
For the tunnel, approximate its water as an infinite uniform cylinder with $R=3.5\,\mathrm m$ and <density> $\rho=1000\,\mathrm{kg\,m^{-3}}$. The bob is at radial distance $r=R+1.5\,\mathrm m=5.0\,\mathrm m$. A coaxial <Gaussian surface> gives
$$
2\pi rL_cg_r=-4\pi G(\pi R^2\rho L_c),\qquad
|g_r|=\frac{2\pi G\rho R^2}{r}.
$$
For the <plumb-line deflection from cylindrical gravity>, horizontal equilibrium gives $d/L\simeq|g_r|/g$. Draining removes the attraction toward the tunnel, so the bob shifts away by
$$
\boxed{d\simeq\frac{2\pi G\rho R^2L}{rg}=5.23\times10^{-7}\,\mathrm m=0.523\,\mathrm{\mu m}.}
$$
The unchanged rock and ordinary <gravitational field> cancel in the before/after comparison; end effects and mechanical disturbances are neglected.
For the <tidal water loading of a spring balance>, approximate the extra water at high tide as an infinite plane slab of thickness $h=8\,\mathrm m$, with the suspended <mass> above it. The <gravitational field of an infinite plane sheet>, derived with a pillbox <Gaussian surface>, gives added downward field $\Delta g=2\pi G\rho h$. With initial <spring> extension $x_0=mg/k=1\,\mathrm m$,
$$
\boxed{\Delta x=\frac m k\Delta g=x_0\frac{2\pi G\rho h}{g}
=3.42\times10^{-7}\,\mathrm m=0.342\,\mathrm{\mu m}.}
$$
\b[The extension increases at high tide.] These estimates use $g=9.81\,\mathrm{m\,s^{-2}}$ and the stated water-density approximation; salinity, finite estuary geometry and terrestrial tidal deformation alter a real measurement.
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