"Only" (and in some cases "just") is often used in this way as emphasis. The actual meaning will vary, but usually means that whatever follows is less extreme, less significant, less uncommon, or less unusual than you might expect. For example:
My car wouldn't start, but I found it was only that I was out of gas.
Here "only" implies that I expected the problem would be serious, but it turned out to be minor. Another example:
She made a trip halfway across town only to buy some pastries from a bakery she really likes.
Here there is an expectation that, if she is going to make such an effort, she would be expected to buy more than just some pastries.
To start to understand Buddhist thought, only remember the fact that nothing is permanent and everything changes.
Here there is an expectation that Buddhist philosophy might be complicated, so the "only" reminds the reader that it actually is based on a simple philosophy.
In your example, "only" implies less extreme. While it's expected that parents will worry about their children, some people might still think it's unusual. The "only" helps reassure their parents that their concern is reasonable.