All the foreign invaders, coming from the west, that I know of which invaded India (i.e. Delhi Sultanate, Mughals, Suri Empire, Ghurid Empire, Mamluk Dynasty, etc.) stopped around the Bengal area. Same with most invaders coming from the Burmese side. The same also seems to be the case with local empires (i.e. Harsha Empire, Gupta Empire, Maurya Empire, etc).
Only exception was the British Raj and the Bengal Sultanate.
Is there any significant reason for this? Bad terrain? Bad weather?
The region to east of Bengal is Myanmar. In between them, the Himalayan foothills taper off rather abruptly into the Bay of Bengal. They still form quite a formidable obstacle. Southeast Asia itself is an isolated place with rugged terrain. I'm not an expert, but it looks like pre-modern civilizations there were located along waterways, and depended heavily on them for mobility.
Myanmar primarily consists of the Irrawady Valley, a large river valley emptying into the Bay of Bengal. It was the first place in Southeast Asia to be significantly connected to the outside world because it was located along the trade route from East India to China. Burmese people migrated here around 200 B.C., until being conquered by another Burmese people around 800 A.D. Both of these people were located on the Tibetan Plateau before migrating into the region from the north.
The first people, the Pyu, began the earliest known civilization in the Irrawady Valley, c. 200 B.C.-800 A.D. As I already mentioned, it was based along the trade route from East India to China. The Pyu were described by 8th century Chinese authors as being monastic and unwarlike. Based on this description, it can be assumed that the region was still isolated and idealic in the 8th century.
The Khmer Empire (802-1452) was the high point of pre-modern Civilization in Southeast Asia. Cambodian Legend suggests that a dynasty of Hindu Kambojas were the founders the Khmer Empire. Kamboja is also the name of a Scythian people in Northwest India who received mention in the Mahabharata. The Sdok-Kok-Thom inscription, written in both Sanskrit and Khmer, describes the founding of Khmer by the Kambojas, and the lives of the first twelve Khmer Kings. The modern name of Cambodia is derived from the Sanskrit Kampuchea, which means the "land of the Kambojas".
There is a saying that "where goods can go, so can armies". The inverse of it is probably your answer. Central Asia (including Northern India) and Southeast Asia are only connected by maritime routes. An invasion of Southeast Asia from India would have had to have been by sea. South India, on the other hand, was adjacent. It was also a lucrative region to invade, being the global entrepot of luxury goods.
It's mainly because of terrain. Between Bengal and Burma there are Himalayan foothills. Hundred of Kilometer long dense forest and high hills made it virtually impossible to mobilize troops in large group, especially in ancient and medieval time.
British Raj is able to conqueror Burma because British Empire is a Maritime Empire, unlike the other Empire in Subcontinent(i.e. Mughal Empire, Gupta Empire, Maurya Empire, etc) which are basically land Empire. British use the sea for troop mobilization and logistic, by which they able to overcome the natural barrier between Bangla(Bengal) and Burma. And also British have far superior technology than Burmese.
Through south-east Asia in never been a part of any south-Asian based empire but the founder of many south-east Asian dynasty have there ancestry back in south Asia. Who either go from Bengal by land or sea, or from south India by mainly sea.
The terrain between India and Thailand was mostly rough hilly terrain and dense jungle, with population living in valleys along the rivers. The Burmese were though fighters, they had been fighting the Thais for centuries. So invading from the direction of India was not exactly a walk in the park. Invaders also had to bring all their supplies from India. Again, not something easy to do.
On the other side was France busy colonizing, in Vietnam, Cambodia and Laos. Thailand had the luck of laying exactly on the edge where both zones met. They had capable kings (Kings Rama IV and V) who played off both colonial powers against each other. That's why they were able to stay independent.
Burma didn't have that luck. Their country was firmly within the zone of British influence. They also had the bad luck of having quarrels within the royal family that didn't help them but were very helpful for the British.
In a nutshell:
The Thais and the Burmese had been fighting against each other for centuries. Both were pretty aggressive and capable fighters. Invading Burma was very difficult due to long communication lines, difficult terrain and dense jungle.
The people who already lived there were very warlike, had centuries of experience in fighting in exactly that terrain. They also had much shorter communication lines.
And on the other side was France busy colonizing.
The usual route wasn't straight east, but along the rivers, southeast.
Could have been done if it was seen as profitable. Tamils only interfered in this region when their trade interests were thwarted. You have the invasion of Indonesia and South Thailand in response by the cholas. Other than that Indians, like the Chinese were not interested in expansionism for it's own sake.
Any invasion had to be done by sea. Even the Mughals had trouble subjugating the ahom dynasty of Assam. Then you had Arakan, Pegu and the land supply lines would be stretched too thin.
India was never ruled by a naval power in the middle ages. It was either fragmented or united by a land based power up north. It's possible that had the Marathas united India, they might have transitioned to overseas conquest but it's unlikely. SE Asia was simply not a very important part of the world for most of history as the terrain limited large populations and as long as indians could trade we were content with staying home.
