β-Variational autoencoders (β-VAEs) are important for reduced-order modeling because they learn compact, nonlinear latent representations that capture the dominant flow dynamics more efficiently than classical linear techniques. By introducing the β-regularization term, they promote disentangled, near-orthogonal latent variables, thereby improving the interpretability and stability of the reduced system. This balance between reconstruction accuracy and regularization enables ROMs that preserve essential physics while substantially reducing computational cost (see [1]). The β-VAE loss function involves two terms: the data loss and the KL-divergence. The balance between them is traditionally achieved by annealing, as introduced by Bowman et al. [2]. We discuss here treating the balancing of the loss function as a multi-objective problem, inspired by PINNs [3]. We implement and evaluate two strategies to balance the terms in the β-VAE loss function: ReloBRaLo and SoftAdapt. Tests in Rayleigh-Benard problems at high Rayleigh numbers (Ra=106 and Ra=1010), taken from [4], show that adaptive β-VAEs keep the Frobenius norm and the orthogonality measure in the same order of magnitudes as the best annealing schemes [2], without the extra burden of selecting the annealing warm-up parameter (β). Moreover, pointwise absolute temperature error measures indicate that selecting adaptively the loss weights adds robustness to the ROMs based on reconstruction in either β-VAEs or Convolutional β-VAEs. Additionally, following the work on [5], we assess the adaptive β-VAE ROMs ability to capture coherent structures on data submitted to lossy data compression.