lme ignores variance function

Question

I am trying to create a linear mixed model for longitudinal data using data that looks similar as the data in the following:

> head(df, 10)
   ID   S  A    BT AT outcome Time
1   1   0 0.40  0  5      90    4
2   1   0 0.40  0  5      90    6
3   1   0 0.40  0  5      90    7
4   1   0 0.40  0  5      90   11
5   2   0 1.32  0  7      90    5
6   2   0 1.32  0  7      90    7
7   2   0 1.32  0  7      90   11
8   3   1 5.78  0  3      85    0
9   3   1 5.78  0  3      85    2
10  4   1 5.98  1  3      58    2

The data is unbalanced in the sense that a different number of observations exists for each subject with irregular time intervals. Unfortunately, with the data as specified in the former, a model with random slopes (or other more complex random structures) does not converge, however I added the data for illustration of the real data, since the real data looks similar.

When trying to fit a model using nlme::lme() with e.g. random intercepts and slopes, a correlation structure and a variance function on the real data, the weights argument is ignored and summary returns the model without taking into account the variance function.

An example:

#(1)

model_lme <- lme((outcome ~ S + BT + A + AT*Time, random = ~ 1 + Time|ID,
                method = "REML", data = df, na.action = na.exclude,
                weights = varIdent(form = ~AT),
                correlation = corCAR1(form = ~ 1 | ID),
                control = lmeControl(opt = "optim")
                 
)

gives the exact same results as:

#(2)

model_lme <- lme((outcome ~ S + BT + A + AT*Time, random = ~ 1 + Time|ID,
                method = "REML", data = df, na.action = na.exclude,
                correlation = corCAR1(form = ~ 1 | ID),
                control = lmeControl(opt = "optim")
                 
)

This happens only for VarIdent, since the model does not seem to ignore e.g. VarExp when using weights = ....

However, when specifying no weights and no correlation, e.g.

#(3)

model_lme <- lme((outcome ~ S + BT + A + AT*Time, random = ~ 1 + Time|ID,
                method = "REML", data = df, na.action = na.exclude,
                varIdent(form = ~AT),
                control = lmeControl(opt = "optim")
                 
)

the model runs for much longer, has lower AIC in my case than the models without this specification of the variance function, and explicitly returns

Variance function:
 Structure: Different standard deviations per stratum
Formula: ~AT | ID 
# Followed by parameter estimates for each unique ID, one value per ID. 

in the summary output.

What happens in model #(3), happens not only for VarIdent, but for all of the variance functions, so I am assuming that I am misspecifying something here. Therefore, I would like to check whether I understand correctly what I am trying to specify:

When using model #(3), the summary output gives me Formula: ~AT | ID, which to me would indicate that for each value of AT (which is continuous), grouped by ID (since it is the within-group variance), a different residual variance is estimated. For VarExp, this would result in Formula: ~AT, indicating that the variance of the residuals increases exponentially for the values of the covariate AT (regardless of the grouping?).

Therefore, I have two questions: (1) Am I understanding the meaning of the variance functions correctly, and (2) What could be happening with the model specification that it takes so long to run in model 3 (also with e.g. VarExp), and the variance function VarIdent is ignored when using weights = ...?