How to reply when she says she's swamped with a project and will text when free

A deadline is a deadline, and in most cases she is exactly as busy as she says. The better signal is the history before this message. If she has been replying within a few hours, asking you things back and picking up threads, then a work crunch is just a pause in something active. If the conversation was already thin, with one word answers and long gaps, then the project is probably the excuse that let her stop without being rude. You don't need to decide which one it is. You just need to notice, because it tells you how much patience to put in and how much to read into the quiet that follows.

Also notice whether she offered a time frame. "Hopefully this weekend" is a soft promise. It is fine to take it at face value and then let the weekend pass without treating a Monday silence as a betrayal. Hold the promise lightly, the way she offered it.

Your reply should show you understood the situation and then stop. A reply that names the deadline, wishes her luck, and leaves no question hanging is the cleanest version. The reader should be able to tell that your message asks nothing of her and that it is perfectly fine for her not to answer until she's free. The move is to make it easy for her to come back later without owing you a response now.

What to leave out is any new topic that needs an answer, any question about her week that she'd feel obliged to answer while buried, and any remark about the plans you'd made. Those turn a kind acknowledgement into a request she has to juggle. Keep it short enough that she could read it on her phone between two meetings and feel nothing but a little warmth.

Once the reply is sent, the next thing that tells you anything is what she does when the crunch eases. If she comes back within a day or two of the stated window and picks up the thread with some warmth, that's your answer and the project was the whole story. If the weekend comes and goes with nothing, you have a judgement to make, and the reply you sent earlier should not be the thing you revisit.

Give it one clean follow-up if the window has clearly passed, short and light, with no guilt and no reference to her earlier promise. Something that only checks in. If that also gets nothing, let it rest. Two unanswered messages after a stated busy stretch is enough information, and a third one only makes you look like you're keeping score.