This is a tough one.
My thinking has actually changed on this one. In the past, my answer would have been no. It's not mentally healthy to weigh everyday. It's obsessive. The fluctuations will drive people crazy and will cause them to give up too easily on their goals.
My thoughts have changed.
For 12 weeks, I weighed myself everyday. At first, I hated it. No, seriously. I hated it. But, knowing I was going to do this everyday for 12 weeks, gave me some real world experience and changed my perspective on the subject.
Yes, the scale fluctuates. This happens for many reasons. The amount of sodium in your system. water weight, inflammation, muscle soreness, hormones, the list goes on and on. Your weight can actually fluctuate up to 5 lbs., although, admittedly, I have not personally experienced that much of a discrepancy.
However, weighing everyday, I was able to come to terms with the fluctuations and began to understand my body better. I knew almost immediately upon waking if the scale would be up or down depending on how much sodium was in my meal the night before, what time I ate my evening meal, and so on.
The other benefit of weighing everyday is that the "fear of the week long let-down" goes away. When I've tried to drop weight in the past, I would look forward to my weigh-in day hoping to see a 1-2 lb. loss. I would build it up in my head, so much so, that I had butterflies in my stomach on "weigh day," Inevitably, the scale would let me down, I would become frustrated, and contemplate throwing it out the window.
It would ruin my entire day.
Weighing everyday, however, you see the trend. Weight loss/gain is NEVER linear. There will be fluctuations, good days and not so good days, and if you only weigh in once a week, you may very well weigh in on a "bad" day.
I should also mention that after my 12 weeks were up, I did take a two week break from the scale. I needed it mentally, as I didn't want to become obsessed with checking or get burned out from tracking. I paid more attention to how my clothes felt, how I looked in the mirror, and continued tracking my food. Two weeks later, my weight was right where I expected it to be....within 1-2 lbs.
My recommendation is this - do what you're comfortable with and realize that the scale is only ONE of the tools you can use to measure progress. Take photos, take measurements, and track your food. Use all the data, including the scale, but not ONLY the scale, to determine whether you are succeeding.