Can a standardized regression weight exceed 1.00?
The mathematical answer is no, it shouldn't. Standardized estimates should always have an absolute value that does not exceed 1.00. However, in practice, there are common exceptions that happen in measurement modeling and in structural modeling. In measurement models (EFA, CFA), when the standardized coefficient between the indicator and the latent factor exceeds 1.00, we call this a Heywood Case. In an EFA, this is no big deal. You can simply ignore it or you can suppress it by using Varimax rotation. In CFA, here is one option: 
In structural models, this can happen when one or both of the variables connected by the offending path are highly non-normal or violate some other assumption, such as using nominal variables without breaking them up into dummy variables. This can also sometimes happen when there is very little sample size (and so a lot of error). Another common cause is if there is extreme multicollinearity between predictors. However, this points to another issue (multicollinearity) that should be resolved prior to proceeding.