poor drainage caused by issue with a vent ??

My bathroom; Sink, bath tub/shower drain via 1.5 to a common 3 inch iron cast pipe.... which also has 3inch cast iron coming from a toilet

Toilet runs great - no issues whatsoever, however, both sink and the tub drain very slowly....and occasionally I see air bubbles escaping.

I tried liquid plumber and similar products about 3-4 times and no major improvement, though each time there would be slight improvement that lasted just a week or so....

I moved in to this house recently and the issue was like that from the start so I can't shed any light about history.
I am thinking maybe the pipe from sink and bathtub are corroded since they are also cast iron and only 1.5inch and the 3 incher from toilet is still enough opened to work OK.

However, a friend of mine said there may be an issue with the vent....
Before I go up on the roof and try to make sure it is not clogged - is this even a possibility ?

Thanks!