Ringo Starr had a song titled “You’re Sixteen” from 1973 and Dr. Hook had a song titled “Only Sixteen” from 1972. What was going on in the early 70s (and prior) with adults dating 16 year olds? Was this normal?

I can shed a little light on the Ringo song. It's actually a cover of a 1960 Johnny Burnette hit, who was the frontman of the Rock & Roll Trio. "You're Sixteen" was written by the professional songwriting pair the Sherman Brothers, most famous for their work with the Walt Disney Company ("It's A Small Word", Mary Poppins, The Jungle Book). The brothers started out as ad hoc songwriters, and sold their first song to Disney, "Tall Paul" in 1958, which was recorded by the budding Mouseketeer Annette Funicello, and climbed to #7 in the Billboard charts.

Between jobs for Disney, they'd try to sell any song they could, and "You're Sixteen" was one of them. According to an interview with Richard (Dick) and Robert (Bob) Sherman published in the September/October 1996 issue of Performing Songwriter magazine, and available on the magazine's website:

[Interviewer]: When you were writing pop and rock n’ roll songs like “You’re Sixteen,” did you feel like you’d found your niche?

Dick: You know, in those days we were just trying to make a dollar. Write a good commercial song that “a kid would give up his lunch money to buy,” to quote our dad (laughs). We were doing the best we could and we got lucky with a wonderful little girl named Annette Funicello. She was 15 years old, she had five months to go on her Disney contract and they were looking around for some material she could sing for the pop market. And a little song we wrote called “Tall Paul” came across the eye of a fellow called Mo Preskell in New York City, who was working for Disney. Annette made this record and it was tremendously successful, and the guys who ran the record company were wonderful. They called us and asked for more material for Annette. Nobody had ever asked us for a song in our entire lives. It was 10 years of writing pop music and all we’d ever had was people say, “Oh no no, we don’t need that, we have too many ballads, thanks very much, but no.”

A similar story is told in the 2009 documentary film The Boys: The Sherman Brothers' Story, which features interviews with both Bob and Dick Sherman. The brothers started writing songs for Annette Funicello, the record company requested more material, and "You're Sixteen" was one of the songs written around that time, when Funicello was just turning sixteen years old. She didn't end up recording it, and so it went to another artist, which happened to be Johnny Burnette. Burnette's version of the song reached #8 in the Billboard charts. It was also at this same time that the Shermans sold "Got The Feeling" for teen idol Fabian to record, though it didn't do quite so well as the songs they'd sold to Funicello and Burnette, stalling at #54 on Billboard.

In 1969, Ringo Starr embarked on his solo recording career, starting with an album of big band covers, entitled Sentimental Journey. The album was a mild success by Beatle and ex-Beatle standards, reaching #7 in the U.K. album chart, and #22 on the U.S. Billboard chart. Ringo followed this up in 1970 with an album of country-and-western covers, Beaucoups of Blues, which flopped. It only got to #65 in the U.S. and failed to chart at all in the U.K.

In 1971, Ringo recorded his first proper, pop-rock single as a solo artist, "It Don't Come Easy", a song co-written by Ringo with ex-bandmate George Harrison. The song was a worldwide Top Ten hit. This was followed by Starr's own composition "Back Off Boogaloo" in 1972, which was once again a worldwide Top Ten hit. Starr then played drums on some tracks of his good friend Harry Nilsson's new album, Son of Schmilsson. According to the 1990 liner notes of the Ringo album by Staffan Olander, it was during the Son of Schmilsson sessions that that album's producer Richard Perry and Harry Nilsson convinced Starr he could record his own proper pop-rock album. They agreed to help him out with the recording and production. In light of his recent chart success, Ringo agreed, and left the novelty records behind.

The album featured eight songs either written or co-written by Starr and one of his ex-bandmates, George Harrison, Paul McCartney, and John Lennon. To flesh out the album, then, Ringo needed some extra songs. The other two songs were a cover of a Randy Newman song, a songwriter who Harry Nilsson was a big fan of. He had recorded a full album of Newman covers a few years earlier, on 1970's Nilsson Sings Newman. The other cover for the Ringo album was the Sherman Brothers' "You're Sixteen".

Ringo was familiar with the song from the Johnny Burnette hit. It had also been a Top Ten hit in the U.K., and the Beatles had previously covered Burnette's "Lonesome Tears In My Eyes" for BBC Radio in 1963 (and eventually released on the Beatles' 1994 album Live At The BBC). In 1969, the Beatles had performed a rather convincing cover of Burnette's version of "Honey Hush" during the Let It Be sessions, even remembering most of the lyrics, which they didn't always do during those sessions. Burnette's material had long been on the Beatles' radar, so with a backing band that consisted in part of Nilsson and Paul McCartney, Ringo recorded a cover of Burnette's "You're Sixteen".

It helped that the song doesn't require an ample vocal range. As Beatles' producer George Martin explained in the 1992 documentary film The Making of Sgt. Pepper when discussing Ringo's song on the album "With A Little Help From My Friends":

"Paul wrote the song, and wrote it beautifully simply, with just five notes that Ringo had to carry, all within one little phrase...Terribly simple, terribly effective."

In the Beatles Anthology book, the interviewees (Paul McCartney, George Harrison, Ringo Starr, and George Martin) also discuss how they would always try to find something for Ringo to sing that was well-suited for his limited vocal range. Thus, the covers he sang for the band weren't all that different from the Burnette cover: "Honey Don't" and "Matchbox" by Carl Perkins, a less-pop-more-rock cover of "Boys" which had been a hit for the Shirelles, and the country-and-western tune "Act Naturally" by Buck Owens.

The song, then, fit the bill of what Ringo was looking for. It had already been a hit song, it fit the pop-rock theme of the album having been written by pop songwriters the Sherman Brothers and covered by rocker Johnny Burnette, and it only required a limited vocal range for Ringo to sing.

As it turned out, it was the right move. Ringo's version of "You're Sixteen" was one of only two songs during Ringo's solo career that has reached #1 on the Billboard chart (the other being "Photograph" off the same album). It was a Top Ten hit in most English-speaking countries as well, and reached #4 in the U.K. Singles charts.

That doesn't really shed a whole lot of light on the overall subject of why there's a lot of teenage lyrics in 1970s rock-and-roll songs. But at least in this case, the reason behind it is that the Sherman Brothers were trying to write songs for Annette Funicello in the late 1950s/early 1960s when she was still a teenager and was singing pop songs aimed at a teenage audience. She didn't record it, but 26-year-old rock-and-roller Johnny Burnette recorded it for his teenage audience, when his record label bought the song from Bob and Dick Sherman. The Beatles were fans of Burnette at the time of its release, and were still teenagers themselves (well, Ringo turned 20 the year it was released, while McCartney was 18, and Harrison was 17). The ex-Beatles still held affection for Burnette's hit tune many years later, so when it came time to find material for Ringo Starr to sing on his debut pop-rock album, the song was perfect for Ringo's vocal range, so he recorded it.