Multi-objectivization transforms a single-objective optimization problem into a multi-objective one in order to facilitate the search for high-quality solutions with respect to the original target objective. This paper focuses on the multi-objectivization strategy of adding a helper objective. Depending on its definition, the helper objective might have a positive or negative impact on optimization. For multi-objectivization to work well, it is essential to select the helper objective with care, according to the nature of the target objective. However, the design of this helper objective remains unclear: should it be completely independent of the target objective or, by contrast, correlated in some respects? We propose and analyze different methods for generating helper objectives with varying degrees of correlation to the target objective, with the aim of guiding the setting of multi-objectivization. Inspired by existing works on multi-objective NK landscapes, we are particularly interested in the joint setting of the correlation between objective-values and the similarity of variable interactions on both objectives. We approximately decompose the target function into several sub-functions based on the Walsh transform. The proposed method combines these sub-functions to create helper objectives with different levels of correlation and heterogeneity. By analyzing bi-objective instances made of a target and of a helper objective under different definitions, we gain insights into the selection of helper objectives depending on the target objective. Our experimental findings suggest that a helper objective with a positive correlation and a smoother landscape is beneficial for multi-objectivization.