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We present an accurate, fast and efficient method for segmentation and muscle mask propagation in 3D freehand ultrasound data, towards accurate volume quantification. A deep Siamese 3D Encoder-Decoder network that captures the evolution of the muscle appearance and shape for contiguous slices is deployed. We uses it to propagate a reference mask annotated by a clinical expert. To handle longer changes of the muscle shape over the entire volume and to provide an accurate propagation, we devise a Bidirectional Long Short Term Memory module. Also, to train our model with a minimal amount of training samples, we propose a strategy combining learning from few annotated 2D ultrasound slices with sequential pseudo-labeling of the unannotated slices. We introduce a decremental update of the objective function to guide the model convergence in the absence of large amounts of annotated data. After training with a small number of volumes, the decremental update transitions from a weakly-supervised training to a few-shot setting. Finally, to handle the class-imbalance between foreground and background muscle pixels, we propose a parametric Tversky loss function that learns to adaptively penalize false positives and false negatives. We validate our approach for the segmentation, label propagation, and volume computation of the three low-limb muscles on a dataset of 61600 images from 44 subjects. We achieve a Dice score coefficient of over $95~\%$ and a volumetric error \textcolor{black}{of} $1.6035 \pm 0.587~\%$.