Speaking as a freelance contract developer myself:
1) normally, they would explicitly say they own the IP to what you build for them
2) it sounds like they did not in this case, but you also did not explicitly say you would charge royalties
3) I don't know what the law says, but the normal way these things work is that if they paid you up front to make it, they own it, and it would give them a lot of legitimate grounds to feel ill-used if you were to find some way to charge them royalties now
4) the goodwill and perhaps recommendations from a satisfied customer, are worth more than whatever royalties you might be able to get out of them, because you probably wouldn't have any goodwill afterwards
By the way, what I have done in the past is have an ongoing agreement of a few hours per month minimum charge (e.g. 5 hours/month) for support, which is not exactly like a royalty. If they don't need any maintenance, great, you write documentation or do security upgrades or whatnot. If they need more than that number of hours per month, they pay you for it, but they agree that you will get at least that many billable hours. But, this would be something for a future piece of work, it would be hard to do it now.
1) normally, they would explicitly say they own the IP to what you build for them
2) it sounds like they did not in this case, but you also did not explicitly say you would charge royalties
3) I don't know what the law says, but the normal way these things work is that if they paid you up front to make it, they own it, and it would give them a lot of legitimate grounds to feel ill-used if you were to find some way to charge them royalties now
4) the goodwill and perhaps recommendations from a satisfied customer, are worth more than whatever royalties you might be able to get out of them, because you probably wouldn't have any goodwill afterwards