This question assumes your table rules that the echo of the echo knight can grapple. Purely RAW, I would not ask this.
Say you are a medium creature and you want to grapple something gargantuan, like the Tarrasque. Using a potion of growth, you can make the echo knight Large. Then, they would manifest their echo which is also Large. Finally, using Enlarge/Reduce you can target the echo to make it Huge. Could that echo grapple the Tarrasque?
Assuming your DM allows grappling with your echo, then yes, its size will determine what you can grapple with it. The grapple rules (PHB p. 195) state
The target of your grapple must be no more than one size larger than you, and it must be within your reach.
So to grapple a Gargantuan creature like the Tarrasque with your echo you will need a Huge echo. Your echo will be of the same size as you, so for it to be Huge, you will need to be huge, EGtW, p. 183:
It is the same size as you, and it occupies its space.
However, your current plan to get that has two different problems:
The Echo is described in the following way:
This echo is a magical, translucent, gray image of you that lasts until it is destroyed
While it shares some aspects of a creature, like having an AC and hp, so does for example the Unseen Servant, and that is also not a creature.
Enlarge/Reduce says
You cause a creature or an object you can see within range to grow
If the Echo is neither a creature, nor an object, it cannot be the target of Enlarge.
Jeremy Crawford has tweeted that he considers the Echo to be an object:
An Echo Knight's echo is an object. It's a translucent, gray image that occupies space; it isn't a creature; and it can be targeted. Object.
Jeremy's answers are not always reliable, and are not considered official rulings any more. In this particular case, his conclusion is highly questionable based on the games definition of what an object is:
For the purpose of these rules, an object is a discrete, inanimate item like a window, door, sword, book, table, chair, or stone
You will have to clear with your DM if you allow the echo to be treated as an object because you want to follow his intention. Rules as written, I think it pretty clearly is not an object.
It also very likely would not work, if you cast Enlarge on yourself after drinking that potion of growth, to become Huge first and then create your echo, because the potion states:
When you drink this potion, you gain the "enlarge" effect of the enlarge/reduce spell
And there is a rule for combining magical effects on page 205 PHB that states the same spell can affect you only once:
The effects of the same spell cast multiple times don't combine, however.
There is another, more general formulation of this principle in Xanathar's (page 5), too:
when two or more effects have the same proper name, only one of them (the most powerful one if their benefits aren't identical) applies while the durations of the effects overlap
So unless your DM rules that drinking a potion to gain the Enlarge spell effect does not count as casting the spell or as the same effect, and can be combined, that will not work.
You would need to find another way to become larger that can be combined with Enlarge.
So, rules as written all these aspects are highly doubtful — whether you can grapple at all, whether you could target the echo, and even if you could, whether you could combine Enlarge effects. But, whatever floats your and your DM's boat. If you all think this is more fun, they can rule it to work.
One way to do it without as much fudging would be the the magic item Potion of Giant Size from Storm King's Thunder.
When you drink this potion, you become Huge for 24 hours if you are Medium or smaller, otherwise the potion does nothing.
This would get you to Huge size in one step. Happy grappling.
