In most of the existing benchmark generators for combinatorial optimization, one cannot tune variable importance, making the generation of real-like instances challenging. However, when it comes to the study of optimization algorithms or new problems there is a lack of real-like instances. To achieve more real-like instances, a recently proposed generator, PUBOi (Polynomial Unconstrained Binary Optimization with importance), includes parameters that directly influence variable weights. The parameters of this generator enable the generation of landscapes with varying properties, such as ruggedness and neutrality levels, yet their global structure and the impact on optimization algorithm behavior remain to be studied. In this work, we use local optima networks to observe the differences in the landscape's global structure according to variable importance. Both the visualization and the metrics highlight how the landscapes are affected by the variable importance parameters of PUBOi, and that landscapes with variable importance resemble real-like ones previously observed. We also conduct a first performance analysis using two iterated local search algorithms and observe different behaviors on different PUBOi instances according to variable weights distribution.