  We construct marked Gibbs point processes in $\mathbb{R}^d$ under quite
general assumptions. Firstly, we allow for interaction functionals that may be
unbounded and whose range is not assumed to be uniformly bounded. Indeed, our
typical interaction admits an a.s. finite but random range. Secondly, the
random marks -- attached to the locations in $\mathbb{R}^d$ -- belong to a
general normed space $\mathcal{S}$. They are not bounded, but their law should
admit a super-exponential moment. The approach used here relies on the
so-called entropy method and large-deviation tools in order to prove tightness
of a family of finite-volume Gibbs point processes. An application to
infinite-dimensional interacting diffusions is also presented.
