You can scale the effect of the whole blend shape itself on the base object. For example, if the cumulative effect of the target shapes deforms the base object more than you want, you can scale down the overall blend shape deformation effect by setting the Weight to a value between 0 and 1.
Select a blend shape deformer (blendShape node), then do either of the following:
The slider specifies values from 0 to 1, but you can enter values from -2 to 2. If the Weight value is 2, the influence of every target shape is doubled; if it's 0.5, the influence of every target shape is halved. If the Weight value is negative, the influence of every target is inverted.