Hello - My parents are from the Mediterranean. I see may Greeks overweight (or moderately overweight) even on the traditional Mediterranean diet since its high on oil (albeit olive) and dairy (espcially cheese), and often grains, and honey too.
Since you live in Greece, you should seriously consider eating the plentiful wild greens available - like vlytra and horta and stifno - every day (without the oil). They provide shocking levels of calcium and iron, with very low calories (if your not drenching them with oil).
I don’t follow the Mediterranean diet anymore because it kept me from my perfect weight. Instead, I follow the "Eat to Live" diet and lost the last 15 lbs and I feel I can follow this diet and eating plan for the rest of my life. “Google it” and you'll see the meal plans.
Even in the US, I go to Asian markets and find “vlytra”. Also, I love swiss chard, dandelions, kale and escarole.