I think
@catinahat covers this nicely.
If we think of food a fuel.
Everytime as T2D, because we are compromised in utilising & converting carbohydrates.
We need a little extra help to shovel away & convert the carbs in our meal choices,
( something that happens more efficiently for those none type 2 )
That extra assistance helps in trying to prevent the excess, sloshing around & being the cause of fatty layering up in places it's perhaps meant AND places it's definitely not meant to be.
So any exercise makes a call out for energy, aka glucose etc.
The premise for T2D management as I see it (as in LCHF) is the less we put in, the less we need to be rid off.
So that exercise for us, is about:
A. Shifting the latest influx of carbs.
B. Scavenging any deficit from the meal, by using up the fats previously layered up in all those nooks & crannies over the years before DX
Thus making our management of the condition as pro active as possible in reducing possible complications from a disease many see as inexorably progressive.
And lifting weights makes the biggest call on our muscles, for that energy which uses up the glucose at a higher rate then other exercises.....
So popular theory goes
Which I think makes sense
Consider the fuel needs of heavy lifting manual work v lighter more sedentary office work, maybe ?
Which would require more fuel to be consumed in relation to the workload.
Which I think indicates the fuel being used up, in each scenario.
Btw, Congrats on trying all the variants you are.
Any exercise (gym or elsewhere) all helps.
And many health benefits to be had with such a broad based training regime, I'd say.