I'm not an expert on the ancient Near East at all, but I was recently reading about some Akkadian recipes found on clay tablets from around 1700 BCE that might help shed some light on this. I think it would be hard to say for sure whether Akkadian cuisine was very heavily spiced, because the recipes don't give amounts (they’ll just say 'add mint' rather than a specific amount of mint, for example) but certainly they knew how to use spices for flavor.

It's worth noting that the recipes on the tablets are fairly elaborate and many are time-consuming. Likely they were intended for the temple or palace elite, so it's probable that the ordinary Akkadian diet was much simpler. I’ll post some examples, as translated by the late Jean Bottero (PDF). Samidu and suhutinnu may have been types of onions. Surummu can’t be identified, but from context it was likely a herb or seasoning.

Red Stew: You do not need meat (?). Prepare the water. Throw in fat. Pluck, tripe, and belly, salt, hulled malt, onions, samidu, cumin, coriander, leeks, and surummu crushed together. Before placing on the fire (in the pot) the meat should be marinated in the blood which has been saved.

Tut’u Stew: There must (also) be the flesh from a leg of lamb. Prepare the water. Add fat [text damaged] salt, beer, onions, (an herb called) spiney, coriander, samidu, cumin, and beetroot to throw into the pot. Then, crush garlic and leeks, and add them. Let the whole cook into a stew, onto which you sprinkle coriander and suhutinnu.

Pigeon Stew: Split the pigeon in two. There must also be meat. Prepare water. Throw in the fat. Salt, hulled malt, onions, samidu, leeks and garlic. All the herbs should be softened in some milk (before adding them to the pot). To be presented for carving.

Other recipes call for mint and juniper berries. Garlic, leeks, and onions are virtually omnipresent and the dishes are prepared by boiling in water (stew may be a bit misleading as a label however, as implied by the end of the pigeon recipe above). The recipes are taken from just three tablets, so it's hard to say if they were typical of Akkadian elite cooking, but they seem like a good insight how spices were used at the time.