It all pretty much comes down to timing.

On paper, the England of Harold Godwinson was stronger than the Norman invaders.

We have wildly differing estimates on the size of the Anglo-Saxon host that fought at Hastings, I've read ranges from 4,000 to 13,000 men. There are also frankly comical Norman sources that state 400,000 to 1,200,000 on the Anglo-Saxon side. But we do know one very important fact, the Anglo-Saxon king had left a great part of his army in the North, including the forces under the brothers Morkere the Earl of Mercia and Edwin the Earl of Mercia. The brothers weren't disloyal to Harold, but they had just fought the Norwegians for control of their Earldoms and their was some apprehension regarding the control of their holdings.

In any case, they were not present for the Battle of Hastings, a fact that was compounded by the Anglo-Saxons having fought the Battle of Stamford Bridge, and suffered considerable casualties of around a third of their numbers less than a month before they would engage the Normans.

The marching host managed to recover some of their number in the march to the south but they were far from their full strength. Had Harold recovered his full strength from Stamford Bridge, the outcome could have been far different. The generally more acceptable sources concerning Harold's forces at Hastings puts their numbers around 8,000 while the combined army at Stamford had numbered nearly twice that number.

The Conquest of England by the Normans was a matter of timing as much as it was one of military prowess. The Anglo-Saxons had no overwhelming weakness that led to their defeat, nor did the Normans have some overwhelming strength that led to their success. Harold had simply been forced to fight too many battles in too short a time for his army to cope.

Sourced from Harold: The Last Anglo-Saxon King by Walker and The Anglo-Saxon World by Higham.

Perhaps something of a tangent, here, but it could be argued that Anglo-Saxon weakness -- or I would rather say lack of purpose -- was responsible for ultimate Norman victory, not so much at Hastings but in those parts of the Conquest that would come after.

Imagine an England determined to fight William. Edwin and Morcar, left in the north, had not been involved in Harold's defeat. London, a large city, could have been held against the Normans. Remnants of Harold's and Morcar's fleets could be rallied to blockade the Normans while a second English army was raised from unaffected areas. Yet instead, the English collaborated, placing William on the throne and only later rising against him due to tensions over WIlliam essentially selling their land back to them.

The problem was one of willpower and united purpose. Who but William would they announce as their king? There was a possible claimant - Edgar the Aetheling - but he was viewed as a poor candidate, and himself hesitant to raise arms against William, instead submitting to him. There would later be much favour for inviting a Danish king Swein to rule leading to an actual invasion and the Normans' worst defeat in England, but they too had little heart for the endeavour, and would eventually be bought off.

Sourced from The English Resistance by Peter Rex.

How are you defining 'strength' and 'weakness' in this context?