The Official Encyclopedia of Bridge says

A prototype of the Weak Two was used in auction bridge and incorporated into the Vanderbilt Club system. Subsequently Charles van Vleck, New York, was responsible for an ultra-weak two-bid. Howard Schenken developed the modern weak two-bid along lines similar to Vanderbilt's.

The note is not specific as to who invented the weak two (or where) in an auction bridge context. Vanderbilt was a pioneer of Contract Bridge. His Vanderbilt Club was a very early strong 1 system in the 1920s, and released two level openings for weak use.

The weak two bid in bridge - 1971

The Blue Club, most popular of the three systems used by the members of the Blue Team, is based on the Vanderbilt Club, invented by the father of Contract Bridge, the late Harold S. Vanderbilt, and almost as old as the game of Contract itself. And part of the Vanderbilt arsenal was the weak two bid in the major suit.

Developed in the early 1930's, incorporated into the Vanderbilt Club system, and polished into its present form by Howard Schenken

A prototype of the modern weak two bid was used as early as the early 1930's, but it was not until the mid-40's that Howard Schenken introduced the weak two bid in a form that is recognizable today.

Auction Bridge Play & Problems - 1925/28

Initial bids of more than one
A E Manning-Foster 1925 {revised 1928}

Initial bids of two of a suit at love score are not recommended because there is no settled or conventional meaning in them. Some players bid two of a suit when they hold Ace, King to six of it, and little or nothing else of value.

Confirming that even before Contract Bridge was invented,
some kind of weak-two or two level pre-empt was in use.

Work-Whitehead Auction Bridge Bulletin - 1926

Origin of the Two-bid without Tops
from: "Mr Whitehead's talks"

More than any other bids or conventions of play in present day Auction the various opening bids of two, advocated by different writers or practiced by Bridge players, are inherited from the early days of confusion and experiment that marked the transition from Bridge to Auction Bridge.

In the game of Bridge, popular at the turn of the {20th} century, the Dealer was obliged to name the trump suit or pass the privilege to his partner. The only talking the opponents could do was to double or pass. Hence the research in Bridge concerned entirely the question of what was an average hand and what were the possibilites of finding certain cards and certain strength in partner's hand. On a hand less than average he was supposed to pass on the probability that his partner might hold a stronger hand and could therefore better determine the best bid for the combined hands; but with certain weak hands, that is, hands holding a long weak suit, the Dealer was advised to bid his suit, as with that suit as trumps his hand might be good for several tricks, while at partner's bid it would be useless.

The salient feature of bridge was thus the conception a "bidding hand", that is on which dealer should bid rather than pass. Such a bidding hand might be one two characters - stronger than average, or worthless at any bid other its own six or more card suit

The conception remained in the minds of players when they abandoned Bridge for the new game of Auction Bridge, which is reported to have originated in India and spread quickly all over the Globe ... In Auction there was for the first time a "contract" ... For the first time also the bidding continued undefinitely, all players alike participating, until 3 players had passed in succession

To our modern understanding the genius of the game lies in the opportunity for partnership co-operation, particularly in the bidding; but in the early days {of Auction} such cooperation on the part of Dealer and his partner was heavily handicapped in that Dealer was obliged to bid. This rule was evidently based on the idea that a deal should not be passed out ...

The better players therefore began the practice of not bidding more than one on any hand that held support for a possible takeout by partner ... The writers came into general agreement a the two bid bid should be reserved exclusively to show a long suit lacking the tops ...

The American Theory was to go after game and rubber, collecting penalties when they offered, but showing strength to partner rather than concealing it from opponents ... {the authorities} took the step, in America at least, of disapproving of such two bids entirely.

The last obstacles to informative bidding were removed by the laws of 1915 which abolished the Dealer's obligation to bid, and with it the low spade value ... The Dealer's side was was now placed on a parity with its opponents and the modern game of Auction began

Bids and conventions tried out in the early days of experiment have been preserved by players who have never learned that thay have been discredited. The chief of these is the opening two bid to deny the tops of the suit.

{in all 3 pages of development} Whitehead clearly disapproved of the Weak two style. Interesting to see that until 1915 - spades were the lowest ranking suit.

The principles, Rules and Laws of Auction Bridge 1910

An early version of 2 hearts
Mr. J.B. Elwell 1910

There is no reason for a bid of more than "one heart" with a generally strong hand; nor should a higher declaration be made with the command of the heart suit; for if the necessity arise, the bid can always be raised; nevertheless, the "two-heart" bid is sometimes made to warn the partner that the hand is good for heart alone and, used for this purpose, has some merit. It has an advantage as a protective measure to save game, albeit often at the expense of a small score loss. The bid of "two-hearts" shuts out the opponent's tentative "one no-trump" call, and offers him less scope to show suit strenght. The oppenent will frequently bid "one no-trump" with a hand containting a protected honour in the heart suit and yet one which would admit of a "two no-trump" call. As the bid of "two heart" is one that the player is extremely likely to retain, the dealer should have decided length in the heart suit to justify it.

KQJ9763  6  Q1075  3

J1096432  42  AK  62

The evidence is that players were opening weak hands at the two level well before the first World War, during the early evolution of Auction Bridge.