Decomposition-based multi-objective evolutionary algorithms (MOEAs) are widely used for solving multi-objective optimisation problems. However, their effectiveness depends on the consistency between the problems Pareto front shape and the weight distribution. Decomposition-based MOEAs, with uniformly distributed weights (in a simplex), perform well on problems with a regular (simplex-like) Pareto front, but not on those with an irregular Pareto front. Previous studies have focused on adapting the weights to approximate the irregular Pareto front during the evolutionary process. However, these adaptations can actually harm the performance on the regular Pareto front via changing the weights during the search process that are eventually the best fit for the Pareto front. In this paper, we propose an algorithm called the weight adaptation trigger mechanism for decomposition-based MOEAs (ATM-MOEA/D) to tackle this issue. ATM-MOEA/D uses an archive to gradually approximate the shape of the Pareto front during the search. When the algorithm detects evolution stagnation (meaning the population no longer improves significantly), it compares the distribution of the population with that of the archive to distinguish between regular and irregular Pareto fronts. Only when an irregular Pareto front is identified, the weights are adapted. Our experimental results show that the proposed algorithm not only performs generally better than seven state-of-the-art weight-adapting methods on irregular Pareto fronts but also is able to achieve the same results as fixed-weight methods like MOEA/D on regular Pareto fronts.