  We study a model of random $\mathcal{R}$-enriched trees that is based on
weights on the $\mathcal{R}$-structures and allows for a unified treatment of a
large family of random discrete structures. We establish distributional limits
describing local convergence around fixed and random points in this general
context, limit theorems for component sizes when $\mathcal{R}$ is a composite
class, and a Gromov--Hausdorff scaling limit of random metric spaces patched
together from independently drawn metrics on the $\mathcal{R}$-structures. Our
main applications treat a selection of examples encompassed by this model. We
consider random outerplanar maps sampled according to arbitrary weights
assigned to their inner faces, and classify in complete generality
distributional limits for both the asymptotic local behaviour near the
root-edge and near a uniformly at random drawn vertex. We consider random
connected graphs drawn according to weights assigned to their blocks and
establish a Benjamini--Schramm limit. We also apply our framework to recover in
a probabilistic way a central limit theorem for the size of the largest
$2$-connected component in random graphs from planar-like classes. We prove
Benjamini--Schramm convergence of random $k$-dimensional trees and establish
both scaling limits and local weak limits for random planar maps drawn
according to Boltzmann-weights assigned to their $2$-connected components.
