I am looking at standardized regression weights (i.e., Beta weights). I was thinking of reporting the errors next to the weights in a figure, but upon some thought I was debating whether such errors even exist. I know un-standardized regression weights have standard error parameters, but do standardized regression weights have error terms?
Yes, they exist.
Are you looking at SPSS output, by chance? (I seem to recall that SPSS uses terminology like you are using.) Here is an image of SPSS regression output that I found on the internet:
The standard errors to the left of the
You can get your own standardized coefficients and corresponding SEs, without relying on SPSS to do it for you. You simply standardize all of your variables ($Y$, and all of your $X$'s) by turning the values into $z$-scores. Then run your regression model with the $z$ transformed variables instead of the raw variables. Now what SPSS reports in the
(Congratulations on your wedding.)