Yeah, the MLPNN (multilayer perceptron neural networks) can easily be used to predict the body weight from age.
Especially, the LM (Levenberg Marquardt) or BR (Bayesian regularisation) based MLPNN can be more productive to estimate the body weight from age. However, it's interesting to see how training model accuracy varies for different age inputs having constant body weight output. To make a system more robust, you have to take huge dataset (may be 1000 or more).
Furthermore, the training of network models are implicitly dependent on many parameters like number of epochs, number of layers, number of hidden neurons in the hidden layer and most importantly the division ratio of training dataset.
The procedure to apply MLPNN models are given in following link:
I would recommend you to read my work first (cf. Appendix B- Backpropagation Algorithm, pg.55-56) Research A Comparative Study on Statistical and Neural Approaches for...
I would also recommend you to use MATLAB Deep Learning toolbox(https://www.mathworks.com/help/deeplearning/index.html?s_tid=CRUX_lftnav) and simulate an ANN model to get a better understanding on how the non-linear correlations are modeled. (https://www.mathworks.com/help/deeplearning/ug/perceptron-neural-networks.html;jsessionid=72b4982bbbbe95586c5dfb102a04)
During model training, we subject our model to a set of known samples and a semantic mapping of the input features is drawn, in your case, from Body Weight ---> Age or vice-versa. Based on our model (whether FNN or BPN/MLP), a mathematical abstraction is formulated, basically in the form of equations (not differential equations). We validate these equations with respect to our target and our inputs (in your case, the input is age and target is BW). Finally, we calibrate our model for each sample, to be precise, we change the weight associated with neurons such that the error (actual BW - model BW) is minimum.