What exactly does it mean to be stronger vs weaker in the Force?

Question

I understand that this likely has a different answer depending on original trilogy or afterwards. But what exactly does it mean to be more or less powerful in the Force? One would think that it means that you are capable of exerting influence on the Force to a greater or lesser extent. But I'm not so sure about that.

If we go back to Luke and Yoda training in the swamp, Yoda has Luke trying to lift his ship via Force. Luke whines that it's too heavy. Yoda says that the weight does not matter

Now that's a funny comment when you think about it. Weight doesn't matter? Really? That tells me that whether you are weak in the Force or strong in it, everybody should be able to move Luke's spaceship. So does strength in the Force refer to the number of things you can do with the Force? Or is it a philosophical strength? Or is Yoda saying that because he is strong that the weight does not matter but to someone weaker in the Force it would?

Admittedly tangential here but that comment about weight not mattering always bothered me. As a kid I always wondered: if weight doesn't matter, could Yoda fling the moon around?

Answer 1

When someone is said to be "strong" in the Force, it means that he has a high midi-chlorian count. Qui-Gon explains what midi-chlorians do:

Midi-chlorians are a microscopic lifeform that reside within all living cells and communicates with the Force...Without the midi-chlorians, life could not exist, and we would have no knowledge of the Force. They continually speak to you, telling you the will of the Force.

_{Qui-Gon Jinn, Star Wars: Episode I The Phantom Menace}

In order words, midi-chlorians translate between the Force-sensitive individuals and the will of the Force. In fact, that is exactly how they are described in the Legends novel Darth Plagueis (it isn't canon, but I find the explanation informative):

A common misconception held that midi-chlorians were Force-carrying particles, when in fact they functioned more as translators, interlocutors of the will of the Force.

_{Darth Plagueis, p. 17}

A person with a high midi-chlorian count is better able to communicate with the Force. Imagine you are trying to communicate with someone in a foreign language -- the bigger your vocabulary in the foreign language (akin to more midi-chlorians), the easier it is to communicate your desires in that language. Therefore, a person "strong" in the Force is better able to exert his will through the Force and lift heavy objects or similar.

The Force itself, however, is an energy field:

The Force is what gives a Jedi his power. It's an energy field created by all living things. It surrounds us and penetrates us; it binds the galaxy together.

_{Obi-Wan Kenobi, Star Wars: Episode IV A New Hope}

The Force is so powerful that it literally binds the galaxy together. The Force itself can lift any object -- in that sense, "size matters not". Anyone who can communicate well enough with the Force can move any heavy object. However, this is easier for someone strong in the Force.

Consider another analogy: imagine you are trying to program a machine or robot to perform some work that no human is strong enough to do. For example, suppose you are programming the trash compactor on the Death Star. The trash compactor is like the Force and is able to exert forces no human can. The programming language used to control the trash compactor is like the midi-chlorians. The better programmer you are in that language, the easier it is to write a program to get the trash compactor to do what you want it to do (this is akin to being "strong" in the Force and having a high midi-chlorian count). A person who does not know the programming language at all (i.e. not Force sensitive) will find it impossible to program the trash compactor properly.

Answer 2

Not sure how much this answers so - but for formatting reasons putting here instead of as a comment:

So - just from looking at A New Hope - Kenobi may offer some insight into how this works:

                              BEN
           Well, the Force is what gives a Jedi his power. 
           It's an energy field created by all living things. 
                 It surrounds us and penetrates us. 
                    It binds the galaxy together.

later -

                                 BEN
                    Remember, a Jedi can feel the Force 
                     flowing through him.

                                 LUKE
                     You mean it controls your actions?

                                 BEN
                     Partially. But it also obeys your 
                     commands.

Based on this, one may see the Force as something always there and available, but "strength" in the Force relates to how well you can perceive and interact with it. Especially applicable is the statement

"A Jedi can feel the Force flowing through him" - this seems to be in contrast to a non-Jedi who then by definition would 'not' feel the Force. Thus, this interaction with and perception of the Force (as seen when Luke perceives Ben communicating with him in the X-Wing) resonates to such a degree that other Force users perceive it as well (ie Vader: "The Force is strong with this one")