Slow 1st month, does it get better?

Pretty much covers it. Feeling some appetite reduction already shows the medication is active. Reaching the needed dose will make controlling portions easier but tracking calories is still useful to confirm intake stays controlled.

I tried 1.5 mg during weeks two and three but ended up vomiting bile so I would rather increase slowly. Will attempt again in a couple of weeks.

More precisely 4 mg is a common therapeutic dose. Clinical data do not establish it as a sharp minimum where effectiveness suddenly begins. Trials showed a dose-response pattern with greater average loss at higher amounts yet meaningful effects occurred for some at lower levels. The original poster already notices appetite changes at 1 mg so results at that level remain possible but not guaranteed.

Let's settle on 3 mg then.

Low and slow works for me so listening to your body is key. If once-weekly injections feel too strong then splitting into twice-weekly smaller amounts can help. I did that after struggling with 4 mg and now handle 2 mg twice a week. Combined with intermittent fasting, low-carb keto eating and light exercise I have dropped about two pounds weekly and over twenty pounds total since late December.