Hi Stan,
it's unlikely you can have a good session in 9 knots with an 11m kite on a twin tip @ 84 kg. I'm the same weight and with lots of light wind experience I need at least 12 knots to start moving around in flat water on a twin tip with a 12m kite. It really only starts to be fun at around 15 knots. 18 knots and I start to be well powered, at 20 knots I usually pack down and pull out a smaller kite.
Remember that live wind readings are usually the average wind over a period of 15 minutes or more, and can be inaccurate for many different reasons.
You don't necessarily need a wind meter, I would recommend instead to familiarize yourself with observations around you (white caps and sand movement) and start to associate wind speeds with those observations. (ask experienced kiters and find out if the live wind readings in your area are accurate or not) After a few weeks you should be able to easily and fairly accurately estimate the wind speed in your area.
I'm sure this was covered in your lessons

but in case it hasn't here is something that may help. This may not work for all areas but at least it's a good start.
Unless your app wind readings are much lower than the actual wind, I would say the problem is that your kite lines might be heavily out of tune, more specifically your front lines are longer than your back lines, probably by a good 20cm, perhaps more. This is causing your kite to be overpowered which impacts heavily your wind range. In high winds you loose the ability to depower your kite, hence the feeling of having a kite that is too big and hard to control. In lower winds your kite will backstall (choke) and fall forward in the wind window.
Here is a video to help you fix this problem:
Happy and safe kiting,
Christian