While reading the same chapter I got a bit confused with that same part:
"Weight and inertia are proportional, and on the earth’s surface are often taken to be numerically equal, which causes a certain confusion to the student"
Actually, in the recording, Feynman never said that weight and inertia are numerically equal, so my guess is that it was a mistake in the transcription. What Feynman said is that inertia and weight are proportional quantities on the Earth's surface. If you have two objects, one heavier and one lighter, you will find that the heavier one has more inertia and the lighter one has less inertia. But, that is ONLY in a portion of space with a constant gravitational acceleration, such as in the Earth, with an acceleration 'g'. What does the latter mean? It means that if you take the heavier object to a portion of space with less gravity, such as the moon (with a gravity of 1.62 m/s/s), it will feel lighter, but that does not mean that it has less inertia, it will have the same inertia as in the Earth. That is, it will have the same tendency to resist changes in velocity as in the Earth. Why is that so? Why is inertia proportional to the weight in a constant gravitational field?
Inertia is a property that describes the tendency to resist changes in motion (in velocity, and therefore, to resist acceleration). That tendency, as you are familiar, depends on mass (more precisely, inertial mass, which has the same value as gravitational mass, so they can be used interchangeably). Therefore, although mass is usually defined as an amount of matter, it can also be defined more abstractly as a measure of inertia (as a measure of the tendency to resist changes in velocity). Therefore, since mass is proportional to the weight (the more mass, the more weight an object), and since mass is a measure of inertia, it follows that inertia is proportional to the weight. But remember that the latter is only true in a constant gravitational field.
The takeaway is the following: Inertia depends on the inertial mass of an object, and therefore, regardless of your position in a gravitational field (in space), your inertia will always be the same, because the amount of matter you hold is the same. However, weight, which also depends on mass (gravitational mass, the amount of mass that interacts with gravity; which remember that according to experiments, is equal to the inertial mass) can change depending on your position in a gravitational field, even if your mass is the same.