Every episode I’ve ever seen has the away team walking around like they’re on Earth (for obvious out of Universe reasons). Are there any episodes where the actors pretend it’s difficult to walk around due to higher than Earth gravity or hop around with ease due to lower than Earth gravity?
In Amok Time, Kirk, Spock, and McCoy beam down to Vulcan. None of the actors "pretend that it's difficult to walk around"; but other sources indicate that Vulcan has a higher gravity than Earth, as well as being hotter and having a thinner atmosphere.
This discussion on TrekBBS indicates that there is textual evidence that Vulcan's gravity is higher, where James Blish's story adaptation of the episode calls the shot McCoy gives Kirk a "high-G vitalizer shot". The Star Fleet Medical Reference Manual is also said to reference Vulcan as a high gravity planet.
As for canonicity: the Blish adaptations were commissioned by Bantam Books, who owned the license to publish Star Trek based fiction. He often went "off script" when writing, the above quote being an example. The SFMRM is an official publication of Paramount Pictures.
I think the best that can be said is that there is reasonably sound, relatively canonical basis for stating that Vulcan has a higher gravity than Earth, and that indeed a ST:TOS landing party went there and beamed down, though they did not pretend to be affected by the supposedly higher gravity.
I don't think we've seen a Starfleet away team beam down to a planet with dramatically higher or lower gravity than that of Earth. This is in part because they mostly beam down to M-class planets, and one of the characteristics of M-class planets is that they usually have gravity similar to that of Earth.
There can be some variation though. In the Star Trek pilot episode, The Cage, an away team beamed down to Talos IV, which was stated by an unnamed officer to have gravity 0.9 that of Earth. Conversely, in TOS episode, What Are Little Girls Made Of?, an away team landed on Exo III, which was stated by Spock to have gravity 1.1 that of Earth. In neither instance did the away teams indicate that the gravity on those planets was noticeably different from what they were used to.
There apparently were some populated worlds in the Alpha Quadrant with gravity very different to that of Earth though. In the DS9 episode, Melora, we were introduced to Ensign Melora Pazlar, an Elaysian. As a result of growing up on the Elaysian homeworld, a planet with gravity substantially lower than that of Earth, she found the artificial gravity on Deep Space Nine to be debilitating, to the point that she required a wheelchair to get around the station comfortably. We never really got to see the Elaysian homeworld itself though, aside from a photo which was likely taken there.
This did not involve any beaming down, but it does answer part of your question:
Are there any episodes where the actors pretend it’s difficult to walk around due to higher than Earth gravity
Yes, kind-of. In Learning Curve (VOY), crew members are seen panting after having completed multiple laps around the deck and Tuvok raising the artificial gravity on that deck by 10%. Do note however that the crew members are out of shape and Tuvok (as a former instructor) is basically trying to get their fitness level up with improvised physical education. So it's not clear how much panting would've been involved had the gravity not been changed, but it's strongly implied it was relevant here.
You wouldn't notice if they did. Modern infantry carry 30% of their weight in equipment, and you don't see them finding it difficult to walk; Starfleet is a military organisation¹ and the personnel are supposed to be fit². So any M-class is going to be ok, if the away team carries their usual light equipment load and beaming around rather than yomping, it isn't really going to be worth mentioning anything up to maybe 40% more than Earth.
Gravity can vary a lot - 'significantly' higher gravity suggests the in-universe reason of being asphyxiated as you're too weak to lift the weight of your ribs or passing out as you can't pump blood to your head, but that would be at several times Earth gravity. Significantly lower gravity implies that you don't have as much atmosphere, and so need to suit up or at least wear breathing apparatus; TOS don't tend to go to locations they need to wear suits.
- in the sense that when at red alert, every crew member is expected to be able to fight, rather than having a separate military force within the crew for away teams, boarding or other kinetic actions.
- not necessarily as fit as C20th infantry in terms of carrying packs for multiple days, but certainly fit enough not to be a liability in combat or away missions
They obviously did, but not to the extent that it bothers them. Exceptions being the zero-g or very close to it scenarios.
All M-class planets are somewhat close to Earth gravity. It's part of the definition!
Anything more than 0.5g and less than about 1.8g is handled with nonchalance by the very well-trained crew. As are any except the most extreme of temperature, humidity, and light levels. As Starfleet, they are trained to adapt and function in all sorts of environments.
and most importantly:
- The convert-o-matic cameras used to record their shenanigans filter out all of the weird stuff, makes all aliens look like humans with a dab of face putty, and lip-synchs all alien languages through the Universal Translator. This very effective filter of course hides most of the actual differences of the alien planets from us, the viewers.
edit: about g-tolerances. Those come from NASA studies about human kinematics. Below about 0.5g, we bounce due to leg muscle trigger thresholds. Above about 1.8g, we stumble due to insufficient elasticity in the achilles and other leg tendons. One assumes that personnel will be trained to all gravities where their bodies function adequately.