Jonathon, you're right, it can be a bit of a balancing act between being helpful and being a pest.
In being a resource or the go-to-guy I think it begins at the networking events. One of my favorite questions to ask - "who's a good referral for you?" or "Is there anyone or any service you're looking to connect with?" or "how would I recognize that someone would be a good prospect for you?" These phrases lets them know that you're tapped in and are open to connect them - of course you'll need to truly look to make the connection/introduction.
Another way to be a resource is to have meaningful conversations (not just talk about the weather, sports or current events) and then follow up by sending them an article or item that is in sync with your conversation.
Regarding your question about following up & when it is time to stop - again, it depends on how you're following up. Too often I get networking follow ups that are blatant (& unwanted) sales pitches. I find this disheartening especially when in no way did I indicate more than a casual interest about their product or service.
Following up isn't about selling -- unless they showed interest and you specifically agreed that you would call them.
The follow up is about deepening the relationship - show interest in what they do, ask one the of above questions about who's a good referral for them. If you've had a meaningful conversation the followup is easier because you'll actually have something to comment on.
I think it's also appropriate to share something of your services that's positioned to be of value. I like to add a PS. note "here's a recent article on (topic relevant to your services) that I thought you might find interesting" Make sure the intent is to be helpful - this shouldn't be a link to your sales page or a sales pitch.
So check your motive to follow up - is it to sell or build the relationship?