Is this a correct way to indicate your weight and height : "I'm 66 kg for 1.77 meter." ?
No.
I am 1 metre 77 tall, and weigh 66 kilos.
In BrE, and in our old imperial measurements, it wasn't necessary to mention the words "tall" or "weight" or "height". I would just be able to say:
"I'm 5 foot 5 and 9 stone 7" and everyone would know exactly what I meant.
In metric, that equates to:
"I'm 1 metre 65 and 60 kilos."
I would say that using the metric measurements, that sentence doesn't sound quite as complete so if I were using metric, I would say:
"I'm 1 metre 65 tall and I weigh 60 kilos."