Watering twice a week might be too much water. Even once per week might be overdoing it. These are succulent/cactus plants as you know, and they store their own water. This article is pretty good but it says flattened leaves is a sign of too little light. Has your plant been in this same spot? It should get enough light where you've got it.
Succulents also have very shallow roots. When you water, don't soak the soil. Water shallowly. Looks like the proper pot size. If you get a chance, I would purchase a shallow clay pot the same diameter but only 3 or 4 inches high. Succulents especially like the clay pots because clay sorta 'breathes', plastic well, is plastic. I would also buy a bottle of distilled or 'spring' water instead of watering with tap water. Too many salts in tap water (chlorine and fluoride). Get a matching clay saucer and using tiles or flat rocks prop the pot up to get air beneath the drain hole. 1/4 inch is fine. Never allow your pot to sit in a water filled saucer. No gravel or rocks below the soil and above the drain hole.
What are you doing for fertilizer? Fertilizer should be a simple, balanced fertilizer like OSMOCOTE 14-14-14 that you only give once per YEAR. Seriously, your plant looks very healthy. aloe vera care Do you have a covered patio/porch? Putting this guy outside during the summers or when there is no chance of frost or freezing temperatures would help him to grow larger, faster. Even on a covered porch (NOT in direct sunlight) would give him more sunlight than your window. This helps to make house plants make more food for themselves, gives them a 'boost' so that indoor plants live longer and look better. I used to always put my house plants on my north facing covered porch for the summer. When I had a porch. This place is too cold for them even inside.