PLease, please do NOT just pop round. OMG New Parents just four months in, trying to sort out a whole new life for themselves. Nothing could be worse than someone just popping round.
ONe of my daughters who had a good reltionshop with her MIL - fell out big time with her because that is what she kept doing when a baby was born.
There is no competitions between g.parents, and a baby is for life, not just a few months.
Just be happy that you are seeing this babe reasonably often, as it grows older will probably be more times, provided you do not alienate the parents now.
Be supportive, maybe doing some washng or ironing, etc not just visiting to see babe, but recognising the adults needs.