I have understood that the total loss was decreasing from the following calculation:
>>> def total_loss(loss, eta):
...     loss = torch.Tensor(loss)
...     eta = torch.Tensor(eta)
...     return (loss * torch.exp(-eta) + eta).sum()
... 
>>> total_loss([ 211.6204, 283.3055,  276.5063], [5.0511, 5.0714, 5.0698])
tensor(20.0620)
>>> total_loss([210.646, 281.631, 275.2699], [5.2132, 5.2701, 5.2673])
tensor(19.7656)
>>> total_loss([ 211.3304, 282.8942, 276.3101], [5.3005, 5.4210, 5.4148])
tensor(19.6715)
>>> total_loss([ 211.3207, 282.6045, 276.2361], [5.3320, 5.5211, 5.5101])
tensor(19.6332)

I think that the uncertainties increase in the beginning but begins to decrease after some epochs, as shown in Figure 7 of the paper. You might need to optimize the learning rate.
Because sigma^2 must be near loss, eta can be estimated using the initial losses as
>>> torch.log(torch.Tensor([ 211.6204, 283.3055,  276.5063]))
tensor([5.3548, 5.6465, 5.6222])

I think the maximum of eta is somewhat greater than the estimated value.
Figure 2 of the paper shows the performance depends on weights. The total loss is given by Equation (1) where the sum of weights is 1.
Because I am not an expert of multi-task learning, you should make a new topic about multi-task learning on this site.