"like heights" is grammatically correct and can be used in written English.
You can use it when describing someone's preferences or feelings towards heights. Example: "She has always been an adventurous person and loves trying new things, but she doesn't like heights."
Some dogs don't like heights.
"I don't like heights," he said.
"I'm no mountain climber, and I don't like heights.
"I don't like heights," she said, keeping a healthy distance from the guardrail.
Now, that kind of stuff doesn't even bother me, but I still really don't like heights.
"I don't like heights, so it would have been a second-floor window.
The Arusi, also of southern Ethiopia, make tombstones of like height, ornamented with engravings filled in with red or black, sometimes showing the deceased in rough relief.
But I also remember walking out of the smoke-filled Fillmore East as the sun rose over Second Avenue, after marathon Allman Brothers Band shows, thinking that if the musicians hadn't quite scaled Coltrane-like heights, they had come as close as any rock band was likely to get.
Not when McGwire, the brightest star in the constellation of players shooting toward Maris-like heights, will be on display at Coors Field, that home run haven that sits a mile above sea level.
Much as she did in "Sisters," Ms. Al-Maria distorts the footage vertically, elongating the already imposing architecture to cathedral-like heights and giving the video's few figures an El Greco-esque ethereality.
With his popularity rating soaring to Bush-like heights, Putin has three geopolitical choices: (1) to align Russia with China against the West; (2) to romance Europe and try to draw it away from the U.S. superpower; or (3) to disappoint China and astound Europe by befriending the U.S. directly.
