How we change what others think, feel, believe and do
Empathetic language demonstrates empathy to the other person, that you are concerned about them and 'feel what they feel'.
A simple construct is 'So you...'. When they say something about themselves, typically that they have been busy, stressed, and so on, you reply 'So you...' and add a likely problem that this causes (and which they are likely thinking about).
You can also reflect what they are saying and add the tag question 'Isn't it?', to which they will of course agree.
To be accepted as such, empathetic language should of course be spoken in kindly ways, along with appropriate body language.
Them: I couldn't sleep last night.
Them: I've just been so busy.
Them: I'm so annoyed with her.
The principle of empathetic language is to demonstrate empathy. You may perhaps have already experienced a sense of empathy, but not all of us are endowed well with this ability and have to resort to more cognitive, conscious methods.
Empathy also helps you understand them better and consequently enables you to make decisions and create interactions which will further appeal to them and make them more likely to agree with you.