Noagenda,
It is not easy to illustrate the difference between, she is acting "weird" and she is acting "weirdly" but I'll give it a shot.
-She is acting weirdly lately.
She is an actress and she is acting weirdly lately.
She just joined Wicca and she is acting weirdly lately, casting spells on everyone she knows.
- In the above examples "weirdly" is clearly an ADVERB.
In English you can use two adverbs together, though you should exercise caution as it can sound awkward. I know of no rule restricting their use according to tense.
-She is acting weird lately.
Her behavior is bizarre recently; she is acting weird.
-In this case "weird" is a PREDICATE ADJECTIVE and "to act" is a linking verb.
It is similar to saying:
She's being weird lately... or ... She seems weird lately.
Linking verbs describe no action -- they merely state an existing condition.
The present continuous can also be used to describe longer actions in progress although we may not be doing them "exactly" now.
example:
I am studying to be a doctor.
She is acting weird lately.