The Traveling Salesperson Problem (TSP) is a fundamental problem with widespread relevance in modern applications such as parcel delivery. Still, the factors that determine instance difficulty for state-of-the-art TSP solvers, such as LKH and EAX, remain insufficiently understood. Prior work has focused on constructing instances that are challenging for either of the two solvers based on the runtime required by LKH or EAX, respectively, for finding the optimal tour of the instance. However, such measures do not adequately capture the anytime behavior of heuristic algorithms. To address this limitation, we introduce weighted Anytime Runtime Performance (wARP), a novel measure which explicitly accounts for the progression of solution quality over time. An analysis of instances considered difficult by established criteria reveals their diverse anytime behaviors, ranging from instances where solvers quickly find near-optimal tours to instances where near-optimal tours are not found. These patterns can be captured by the new wARP measure. Leveraging the sensitivity of wARP, we propose a gradual instance generation process that constructs instances that are consistently challenging for both LKH and EAX. This provides an alternative basis for evaluating algorithmic variants and enables a more nuanced analysis of their strengths and weaknesses. Furthermore, the proposed concept is transferable to other domains, providing a foundation for more informative benchmarking and targeted instance generation beyond the TSP.