Question

What was the largest and wealthiest monarchy in Europe by the end of the 13th century?

Answer 1

For the specific date, I'd lean to England. France was very weak at this time. The King didn't control much of the country, and that was even more true in Spain, where there were numerous competing kingdoms, some Muslim. It certainly wasn't Byzantium, which never recovered from the sacking of Constantinople in 1204. The Holy Roman Empire was also going through a rough period at the specified time.

So I would lean to England, currently under a strong King (Edward I, 1272 - 1307) who successfully won for the English crown permanent control over Wales and also control over Scotland, although that was lost by his far less capable son, Edward II. Edward also held extensive estates in France and Spain through his own inheritance and his marriage to Eleanor of Castile.