The automatic segmentation of multiple sclerosis lesions in Magnetic Resonance Images is an open research area aiming to bring more reproducibility in the radiological visual assessment of the disease while reducing the burden of this time-consuming task. The development of artificial intelligence has led to significant improvements in computer aided diagnosis tools for radiology. It exists several efficient approaches for the voxel-wise segmentation of multiple sclerosis lesions using artificial neural networks and convolutional neural networks in particular. However, the small lesions are frequently neglected by those algorithms despite their radiological importance. We propose here an adaptable method to improve the detection of small lesions. The problem of small lesions detection mainly comes from the under-representation of those lesions at a voxel level and the segmentation loss function. The presented method consists in weighting the lesion importance during the training of a convolutional neural network depending on lesion size to correct the impact of voxel lesion imbalances. The designed weighting function is configurable and can be extended to other segmentation problems. With our method, the lesion segmentation computed with the Dice score is only slightly improved but the detection sensitivity is significantly improved at the cost of a limited augmentation of lesion false positive rate. The F1 score has been substantially improved with the correct set of parameters. The improved prediction quality of segmentation maps has been confirmed visually with the help of a radiologist on a dataset acquired in our institution. The described method improves the lesion detection by giving more importance to small lesions during the multiple sclerosis lesions segmentation learning, bringing a more accurate help for the radiologist towards a better impact for the patient care.