One useful thing an attacker could gather is what your response time is at different times during the day and also things like your sleep schedule. If you leave your phone at home when you go jogging or to a meditation class they may be able to determine times at which other entities may not be able to reach you quickly. This may give the attacker knowledge of when to best attack you or your employer. So yes even the response time has value.
The next thing that may be useful is the words you use and your very personal phrases Things like "Thanks again" "Cheers" "Peace" or "Have a great day" may help an attacker forge e-mails for a phishing campaign that look exactly like text you would actually use in conversation.
After that, there is target OS identification. In a nutshell, if the person sending you these is using a device which supports Apple's iMessage protocol they will in most cases, be able to see if your phone supports iMessage or not giving a very high likelihood of telling the attacker your phone's base OS as being either iOS (iMessage supported) or Android/Other (iMessage not supported). This is by no means absolute but if they are collecting this information from a large number of targets it will be mostly accurate data.
A slightly more dangerous and hopefully unrealistic example for conversational purposes, if a Bank were to authenticate a wire transfer via a simple Y or N response from a phone number on file for their poorly written SMS application an SMS could be crafted from a spoofed VoIP number that matches the bank's real source phone number.
If an attacker could time things correctly (again this is an unrealistic example) he or she could initiate a few fake texts to you to determine your average text response speed at 3pm or so then send you a well timed question looking for a 'Y' or 'N' response that is in turn being sent back to the spoofed bank number.
In a nutshell, you get asked something ridiculous like: "Would you like to see an image of me in a sexy panda suit? 'Y' or 'N'?
and that response becomes the reply to "A request to wire $10,000.00 to the national bank of hackerland has been requested do you approve this request? Respond with 'Y' or 'N'?" by the nature of you replying back to the spoofed text to the banking app's source number.
Again this is something of a fictitious example but the combination of insecure SMS systems in some countries combined with some horribly written systems allowing user SMS input something similar to this could potentially be possible.
Architecturally SMS was built before security was a concern, it has almost no security controls to speak of and although useful it should not be used for high-trust applications like authorizing wire transfers.
Even if it seems like fun you are technically giving this person/entity data. If they happen to be malicious and you or your employer are useful targets it might be wise not to respond or in the case of iMessage even open/acknowledge the messages.
Lots of organizations are doing bad things at scale right now. This could easily be part of a large-scale reconnaissance effort.
Possibly useful reference: