Supporting a Local Business Beyond Making Purchases

My small city (pop. 20,000) has a bunch of chain grocery and big box stores, and more moving in all the time.

But--locally-owned shops are also opening here several times a year, including, just down the street from me, a local market. They sell a small variety of local products there, but particularly a two-miles-away-farmer's grass-fed beef--all cuts, labelled and packaged and ready-to-go.

Obviously this is going to be my only source for all beef products from now on--but my purchases are going to run to only $20 or so per week. I can't spend $100s there to keep them open long-term, but I would like to do more for their business.

What are other ways to help keep them open?

Keep doing what you are doing!  Do business with them at your level and mention them to locals like you did to us here.  Good job!

Exactly what Bryan said. You can only buy what you need, but it all helps. Buy what you can, let friends and neighbours know what a great product it is (obviously if appropriate).
Be a nice customer - talk to the staff and let them know how great they are! Feedback on the product. If there is something that would be better for you - bigger/smaller packs, different packaging, delivery, whatever - let them know. Most small businesses are operating on guesswork and don't have a marketing expert. Be a tidy customer, if there's a spill let them know discretely.
I suppose you might be able to advertise on their behalf. In terms of telling friends and neighbours, social media can be a powerful tool, so if there is a local FB page or other local online noticeboard you could share your positive experiences there. Share any media they make online: FB, instagram, whatever. It's hard to get heard on these platforms if you don't have the volume, so local ones will probably be more powerful. If there isn't a local online magazine then maybe you could be the one that starts one.
I don't need to preach to the converted, but shopping locally really does help the local economy. The big guys won't even notice you, but you make all the difference in the world to the small guys like me.

(My little store)

You probably already thought of this, but you could ask them if there's any particularly helpful ways to support them beyond buying more. I think word of mouth is really the best advertising, so obviously that. Social media like nextdoor could be good. Leaving glowing reviews, if they have somewhere to do that.

I've found sharing the food from farmers quite effective at getting people to start buying it themselves. For example, last time I had a meal with my family, I cooked and made a point to talk up the local, sustainably raised meat and the farmer I get it from. My family almost never says anything about stuff I cook. They were all raving about how good the meat was and loading up on seconds. You could do similar if you're sharing a meal with friends or family anyways. Of course, that might not even be necessary if people are already interested in finding better quality food. Just the mention might be enough.

If you have a local restaurant where you like to eat, you could mention how good the beef from this shop is.  That could get them another customer but also exponentially additional ones from the restaurant's customers.  

Post positive reviews everywhere you can.

See if your local business can bring in orders of bulk or restaurant-size foodstuffs for you. If you trust them, put down a 50% deposit. They can probably give you a price that competes with the big boys since they know they don't have to stock it and wait for a buyer.

John F Dean wrote:Post positive reviews everywhere you can.

This I think is increasingly valuable in this digital age. We may moan about the power of google, but I believe that having a good google rating and reviews makes a lot of visitors to our island stop and shop with us, whom previously would have driven past, not even knowing we were here.

Tell your friends, tell your coworkers, tell your neighbors, tell tourists.

Word of mouth is still very valuable.

People come into my store everyday because someone told them about it.