  We investigate the two lowest-lying weakly bound states of $N \leq 8$ bosons
as functions of the strength of two-body Gaussian interactions. We observe the
limit for validity of Efimov physics. We calculate energies and second radial
moments as functions of scattering length. For identical bosons we find that
two $(N-1)$-body states appear before the $N$-body ground states become bound.
This pattern ceases to exist for $N \geq 7$ where the size of the ground state
becomes smaller than the range of the two-body potential. All mean-square-radii
for $N \geq 4$ remain finite at the threshold of zero binding, where they vary
as $(N-1)^{p}$ with $p=-3/2,-3$ for ground and excited states, respectively.
Decreasing the mass of one particle we find stronger binding and smaller radii.
The identical particles form a symmetric system, while the lighter particle is
further away in the ground states. In the excited states we find the identical
bosons either surrounded or surrounding the light particle for few or many
bosons, respectively. We demonstrate that the first excited states for all
strengths resemble two-body halos of one particle weakly bound to a dense
$N$-body system for $N=3,4$. This structure ceases to exist for $N \geq 5$.
