How did the layout of a Medieval European village typically change as it grew into a town?

I would start with a brief explanation on how I'd classify township development in the Middle Ages. I don't expect this to be exhaustive, but rather illustrative of the few lines of development that I can note where cultural reasons might cause some variance from another plan. Please note this is not 'academic' per se, but rather some of the differences I managed to think about right now.

• Roman towns with a generally rectangular plan which continued as important centres throughout the time period (Rome / Paris);
• Roman towns with a generally rectangular plan which would have become depopulated except in a small area (at best) and which would, after then, have been slowly repopulated, if at all, though the main development would have taken place outside the old main walls (London / Chester);
• New Christian towns which developed gradually (Dortmund);
• New Christian towns on locations of old pre-Christian settlements which developed gradually (Riga);
• New Christian towns on locations of old pre-Christian settlements which were developed purposefully (Helsinki)
• New Christian towns which developed around a castle though the castle itself may have been founded in a previous fortified settlement (Åbo);
• Islamic towns which took over existing population centres (mostly Roman towns in Europe) and developed these according to their need (Palermo);
• Orthodox towns would probably have developed around their special lines, i.e. I'm not sure how much market rights were regulated there, etc, so that should be investigated separately.

I would also recommend a look at my answer here regarding how market development affected a village's progress into a town (and which usually took place near a church). As the founding of markets was the source of revenue, these were highly regulated. While unofficial barter marketing probably took place, no lord would have allowed this on a grand scale as in an unofficial market.

In other words, both churches and markets were guiding lights for town development.

But I also wanted to bring some specific examples.

1. Arensburg / Kuressaare

• Started out as an ancient trading post due to its good harbour.
• A castle was founded in 1381. In 1424, a township is mentioned as having developed around the castle, and it gradually gained in importance. In 1612, the town was conquered and most buildings put to fire—rebuilding started from the church. In its gradual rebuilding, one of the newer centers was the weigh house alongside its port warehouses and town hall.
• In the Great Northern War, the town was burnt down again and only one building and (unsourced—I remember reading this a long while ago) about twenty people survived from the whole settlement. I know this goes beyond your timeframe, but I wanted to show that development wasn't just a progress forward, but more often than not the development started anew from some state.

2. Helsinki

• Settlement in the area is known from Iron Age with agriculture from the 10th century and recorded settlement from the 14th century.
• Fishing villages also existed, and Gustav I decided to develop one of these (along with a nearby mansion of his own) purposefully as competition to Reval. Burghers were resettled from nearby centres to this new location, but this generally failed as the location which was chosen had a very shallow harbour and this turned out to be unsuitable for the ever-growing trade ships.
• Hence, the town didn't grow as much as expected and remained insignificant until people decided to properly fortify it in the 18th century (and move to a slightly deeper harbour around the same peninsula). Of course, in this timeframe, the city was burned down, struck by plague, etc.

3. Norwich

• A Roman settlement (the rectangular plan is still visible) of Venta Icenorum was situated a few miles south of modern Norwich on the River Tas into the 5th century. I believe that the primary reason for moving its centre, when it was resettled by the Anglo-Saxons, was that the Tas was (hydrographic changes have been very pronounced in East Anglia) shallower than the Wensum which was chosen as the river for the new centre.
• An important Anglo-Saxon trading site (or perhaps three) developed in the area. A mint was established before 939. Norse attacks sacked the town in 1004, but the area was continuously settled, and an Anglo-Scandinavian district developed.
• Domesday surveyed 25 churches and a population of up to 10,000 in Norwich at the end of the 11th century.
• William started the construction of a castle (and 98 homes were demolished for it), and Norman development focussed to the west of the castle where the present market still exists (as developed by the Normans).
• A cathedral was also built, and the bishop moved his see to Norwich in the end of the 11th century (but maintained extensive castles and properties outside of the city).
• City walls date to 1280 at the earliest. These include a river gate and towers that would enable chains across the river. Development outside of the walls was prohibited.
• Most notable in the history beyond this time is that the city acted as a place of refuge for 16th century Dutch and Flemish refugees (who also settled in their own quarter and who have shaped a lot of the area near St Andrews Hall).

Some illustrations from placards that are up in Norwich (note the Cow Tower was not related to the chain towers I mentioned above, there is a placard by those as well I believe but I've not photographed it):