Use both sample_weight and class_weight simultaneously

You can surely do both if you want, the thing is if that is what you need. According to the keras docs:

• class_weight: Optional dictionary mapping class indices (integers) to a weight (float) value, used for weighting the loss function (during training only). This can be useful to tell the model to "pay more attention" to samples from an under-represented class.

• sample_weight: Optional Numpy array of weights for the training samples, used for weighting the loss function (during training only). You can either pass a flat (1D) Numpy array with the same length as the input samples (1:1 mapping between weights and samples), or in the case of temporal data [...].

So given that you mention that you "have far more of the first class compared to the second" I think that you should go for the class_weight parameter. There you can indicate that ratio your dataset presents so you can compensate for imbalanced data classes. The sample_weight is more when you want to define a weight or importance for each data element.

For example if you pass:

class_weight = {0 : 1. , 1: 50.}

you will be saying that every sample from class 1 would count as 50 samples from class 0, therefore giving more "importance" to your elements from class 1 (as you have less of those samples surely). You can custom this to fit your own needs. More info con imbalanced datasets on this great question.

Note: To further compare both parameters, have in mind that passing class_weight as {0:1., 1:50.} would be equivalent to pass sample_weight as [1.,1.,1.,...,50.,50.,...], given you had samples whose classes where [0,0,0,...,1,1,...].

As we can see it is more practical to use class_weight on this case, and sample_weight could be of use on more specific cases where you actually want to give an "importance" to each sample individually. Using both can also be done if the case requires it, but one has to have in mind its cumulative effect.

Edit: As per your new question, digging on the Keras source code it seems that indeed sample_weights overrides class_weights, here is the piece of code that does it on the _standarize_weigths method (line 499):

if sample_weight is not None:
    #...Does some error handling...
    return sample_weight #simply returns the weights you passed

elif isinstance(class_weight, dict):
    #...Some error handling and computations...
    #Then creates an array repeating class weight to match your target classes
    weights = np.asarray([class_weight[cls] for cls in y_classes
                          if cls in class_weight])

    #...more error handling...
    return weights

This means that you can only use one or the other, but not both. Therefore you will indeed need to multiply your sample_weights by the ratio you need to compensate for the imbalance.

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Update: As of the moment of this edit (March 27, 2020), looking at the source code of training_utils.standardize_weights() we can see that it now supports both class_weights and sample_weights:

Everything gets normalized to a single sample-wise (or timestep-wise) weight array. If both sample_weights and class_weights are provided, the weights are multiplied together.