Congrats on taking those first steps!
Do not worry about HRT only affecting "new weight". Not true. The body redistributes what it has to put it where it needs to be and will take from where it doesn't. If you are losing weight or gaining weight, it doesn't matter. The body will build accordingly and use whatever is available.
Next, examine your motivation here. Is that the true reason for waiting? Be honest with yourself. If you are not ready, then you are not ready. There is no shame in that. The time to start is when you are ready, not because of some imaginary timeline.
You have them handy so you can start when you are ready. You probably already know this, but for the first 30 days, nothing will happen. Body fat will not move, breasts don't spring from your chest, and you won't start naturally swaying your hips when you walk.
What may happen (most likely) is that you will notice a change in your moods. If you notice that you feel down, depressed, irritable, or any sign that something is wrong, STOP immediately. That is a sure sign that you are not ready, and something else is going on. That is the time to check in with the provider and a therapist.
My own experience was that I suddenly noticed (after about 2 weeks) that I was happier. I smiled more. I wasn't grouchy. I had been nicknamed the Crochety Old Geezer, but suddenly that changed. So most of the changes will be mental/emotional, not physical.
It takes six months for things to start changing physically, and that six months doesn't start with the first pill. It starts after your hormone levels are high enough to signal the changes. Then the clock starts. It took me four years to get my levels where they needed to be. So changes started, but they were very slow.
Don't panic yet. Pick a day that you want to be your new birthday and start your dose on that day. If you aren't ready, then wait. This is your life, and no one can live it for you. You get to decide.
I hope this helps.