It depends on the context.
It can be used to describe unusual or odd behaviour - something that makes you feel uncomfortable.
"Somebody on the bus smiled at me today, but in a weird way, it made me feel uncomfortable"
It can also be used to talk about how something has an unexpected and strange/odd effect on something else.
"Even though I can no longer walk, in a weird way I am more active than I ever have been in my life"