The German feminine noun "die See" doesn't mean English "lake" or Dutch "meer". Here are the correct translations:
Ger der See, Ger die See, Eng the sea, Dut de zee
Etymologists are sure that both German nouns "der See" and "die See", the English noun "the sea" and the Dutch noun "de zee" have the same etymological root, but it is unclear what exactly this common root is. Some say it comes from an old word for "water bucket" or "tub". Others think it might be related to a verb that means "to pour" or "to drip", and there is also another old word that sounds similar which means "water collecting in rivulets".
All in all it seams to me as if the ancestor of See/sea/zee was used for smaller amounts of water at the beginning (like ponds and lakes) and then got used more and more for bigger water bodies.
Ger das Meer, Dut het meer
This word was in latin language "mare" and was a synonym for "oceanus" and both words meant the sea, the ocean. But similar words in related old languages meant "bog, marsh" or "morass" (German: Moor, Sumpf, Morast, Marschland) but also pond (Ger: Teich) or puddle (Ger: Pfütze, Pfuhl)
Ger mehr, Eng more, Dut meer
Also these words are cognates and the common ancestor meant "big", "famous", "wellknown". Another offsprings of this etymological root are German "die Mär" and "das Märchen" (Engl: story, fairy tale)
Both word groups around the words ["das Meer", "het meer"] and ["der/die See", "the sea", "de zee"] have been used in many Germanic languages to name bodies of standing water of any size (puddles, ponds, lakes, seas and oceans).
- There is no relationship between German "das Meer" and German "mehr".
- There also is no etymological relationship between Dutch "het meer" (the lake) and Dutch "meer" (more).
- Also German "das Moor" (gob, marsh) is not related to English "more" although they are pronounced almost identically in Received Pronunciation.
- (Also English "the sea" and "to see" aren't cognates)