These days in corporate world it is fashionable to hate meetings, for various reasons. I also belong to that category, I don't like meetings because they force me to stop my workflow and get in sync with team, they doesn't seem to add any value to my productivity. Meetings are usually longer than they are supposed to be. Also i am not a fan of banter that goes on in meeting rooms.
Having no meetings is great and sounds like lot of freedom to the employee , but why is your manager is still pushing for meetings, why is you company management adamant on having weekly meetings.
The single most important reason meetings required is to track status. If you want no meetings and still be as good, the solution is simple. Make status Information transparent & easily accessible to the concerned. If they can get information without you both sitting in a meeting room, you can avoid majority of the meetings.
The Second reason your manager wants meetings because it gives an opportunity to guide each other, seek clarifications from others on issues or simply to facilitation cooperation among the team members. This is a tougher problem to solve than the first one. To communicate, everybody has a preferred mode. Skype calls, instant messaging, emails to name a few. I prefer email for the asynchronous nature of it. Whatever is the mode you use, the important thing is to set an expected Turn around time, being Predictable in your timelines. Other person wont bother you to call for a meeting until and unless you are not sticking to the schedule you defined.
The last point i want to bring is about sharing common vision. Many times we assume as a team there is perfect sync, going forward to achieve the goal and question the point of having a meeting to discuss vision. But it is very easy to make a wrong assumption and take people for granted. Probably even without meetings you can go ahead, but by the time you realize there is a communication gap, it might be too late. The first two points will be easy to overcome but this lack of shared vision can cost a lot to the team. The bottom line is to make sure there are no communication gaps, especially between cross functional and management teams, monthly or quarterly meets are what people usually do.
Some other day we will look at how to keep meetings shorter and productive. Till then good luck browsing your facebook feed in your next meeting