Environ or à peu près are fine translations for like in the first sentence. To state you don’t precisely know how far it is, you might also say:

• C’est peut-être à trois kilomètres d’ici.

For the second one, I would say:

• Ce plat était délicieux, j’ai mangé quelque chose comme deux kilos de viande…

Quelque chose comme is also used in the French expression ou quelque chose comme ça which I believe match the vagueness of the English “like”:

• Ce plat était délicieux, j’ai mangé deux kilos de viande ou quelque chose comme ça…

Note that I do not use miles/livres but kilomètres/kilos in France as the former risks to be confusing if not misunderstood here.

Genre, suggested in other replies, is fine and not only used by French Canadian speakers. However, despite its conciseness, it seems to me more colloquial than the English “like” in that context and far less used than ou quelque chose comme ça (at least in France), the reason why I prefer to advise the latter.

The problem here is that this usage of “like” is very common in English, but has no exact equivalent in French. It is mostly heard, rather than read, because it expresses something different according to the oral context.

I believe that “It’s like two miles from here” is slightly different from “It’s about two miles from here“. In the first sentence, depending on the tone, “like” can be a form of emphasis on the distance, or also insist on the fact that the speaker doesn’t exactly know the latter, making it less trustworthy than an “about” approximation.

So, depending on the context:

C’est à environ 2 km d’ici (simple approximation)

or:

Ça/cela doit être à 2 km d’ici

Notice the use of the verb “devoir“. If you pronounce this last sentence with a neutral tone, it is just an oral form of approximation; but with an exclamation mark, and with the according tone, it expresses emphasis on the distance (“It’s too far away, it’s like two miles from here!“). Further precision: you would say “ça doit…”, but write “cela doit…”.

As for the second sentence, it is more simple to translate.

Ce plat était délicieux, j’ai dû manger 2 kilos de viande !

This is a very common form, and in my opinion it is the best way to translate “like” in this context, as the verb “devoir” here expresses doubt on the ingested quantity in a sarcastic way, as “like” does in the original sentence.

In case you wonder, I am French, so I can tell you these are everyday usages 😉

You could say “genre” in french slang : “c’est genre à 2 miles d’ici” or “j’ai mangé genre 5 livres de viandes”. It would fit with the original sense you mean.
Note that in France, we would say “kilometres” instead of “miles” and “kilos” instead of “pounds”.

I understand your question and I would say that where I live, in Québec(french-Canada), it would be translated as the following
:
«C’est genre à deux miles d’ici.» or «C’est comme à deux miles d’ici.»
«J’en ai mangé genre 5 livres.»
But this is really really much local in Abitibi-Témiscamingue and only millennials talks this manner.
The word “genre” is a new quebecer’s slang for “comme”, “exemple”, “façon de”, “à la” or “style”. It’s colloquial.