They're both grammatical:
Welcome is an adjective which means agreeable or gladly received.
Welcome is also a verb meaning to receive or accept with pleasure. Formed into a past participle, which functions as an adjective, it is welcomed.
More is welcome is definitely the one you want, since it implies to the viewer that they are being targeted by the statement. More is welcomed, on the other hand, sounds like a bare statement of fact that you currently accept more, without the same appeal to the individual viewer.
The quickest source for English etymologies is etymonline.com, which will give you this:
1883, alteration of hallo, itself an alteration of holla, hollo, a shout to attract attention, which seems to go back to at least c.1400. Perhaps from holla! “stop, cease.” OED cites Old High German hala, hola, emphatic imperative of halon, holon “to fetch,” “used especially in hailing a ferryman.” Fowler lists halloo, hallo, halloa, halloo, hello, hillo, hilloa, holla, holler, hollo, holloa, hollow, hullo, and writes, “The multiplicity of forms is bewildering ....” Popularity as a greeting coincides with use of the telephone, where it won out over Alexander Graham Bell's suggestion, ahoy. Central telephone exchange operators were known as hello-girls (1889).
Etymonline's main source, and the “authoritative” English source, is the Oxford English Dictionary. This is in constant process of revision; the current state is available online by subscription, the first edition is available free from archive.org (I give the volume-by-volume links below). Here you will find all the variants above as distinct headwords, as well as a number of variants ending in {-oo}. It offers (s.v. Holla) as another possible source or influence French holà,“stop!, wait!” recorded since the 15th century. Wiktionary s.v. hallo gives parallels in other European languages and suggests that it represents “Old English hēlā, ǣlā, ēalā (“O!, alas!, oh!, lo!”), equivalent to hey + lo.” There's no evidence for the OE connection, but I think it very likely that hey, ha, ho lies at the bottom of all these.
The upshot appears to be that something like /'hVlo/, with a lengthened endstressed version /hə'loː/ or /hə'luː/, has been around since late Middle English (and may go farther back) as a cry to catch someone's attention. Its ultimate origin is obscure.
I think the orthographic variants should probably be regarded as just that: spelling preferences for a word with various trivially different pronunciations. Here is a Google Ngram which graphs the occurrence of the most frequent 19th and 20th century variants against the occurrence of hello; as you see, hello has been for three or four generations the most popular. The crossover came in US English about 1895 and in British English about 1920:
OED 1 at archive.org:
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Best Answer
Greeting someone by saying “welcome in,” is hardly a novelty:
What does seem novel is that you’re hearing it as you enter a shop, especially if it’s in a mall, where you’re moving from one climate-controlled space to another. Traditionally, the greeting is given as someone holds a door for you, especially in inclement weather. The in is directional, i.e., accenting that you’re moving past an obstacle or coming in from rain, cold, etc. If none of these apply, then I would imagine the implied barrier guards what the store employees hope is a pleasant, relaxing, or luxurious atmosphere, at least better than whatever is “out there.”