In-Universe, this is covered by the accepted answer to the related question Wikis linked to.
Blatant copying of the quote:
SILBERMAN: "Why didn't you bring any weapons? Something more advanced. Don't you have ray guns? Show me a piece of future
REESE: "You go naked. Something about the field generated by a living organism. Nothing dead will go."
SILBERMAN: "Okay. Okay. But this... cyborg...if it's metal..."
REESE: "Surrounded by living tissue."
SILBERMAN: "Of course."
This you already knew, given you asked why they couldn't carry something under their skin.
There's no given 'canon' answer, but I do have some theories. We see that the skin of the T-800 can be injured. As we learn in T2, it will heal, given time.
The T-800 chassis (seen above) does not have a significant amount of places where it could store a weapon - the only place with enough room would be in the abdominal area.
The T-800 does not need abdominal muscles to remain standing, obviously, nor would he have been functionally inconvenienced by the opening of this region to retrieve weaponry.
That said, it would have taken a long time for such a wound to heal, and that is an awkward location for the T-800 to treat itself. The T-800 would have required assistance to treat the wound it caused, putting it at great risk of discovery.
The alternative would be to walk around with (what appears to be) a massive stomach wound. This would not have been easily discernible under clothing - assuming clothes could be acquired, but could not have escaped close scrutiny.
So while it would certainly be possible for the T-800 to bring back, say, a small plasma rifle, it would make the task at hand (finding and killing an unsuspecting civilian while remaining undetected) at least slightly harder.
At the time when the T-800 was sent back, it was not aware that the Resistance would be sending back a fighter to protect Sarah - it thought it would face only uninformed humans. Had they not sent back Reese, the mission would have succeeded within the first 12 hours.
Skynet was aware of the ease with which a T-800 could acquire firearms, though maybe not the exact availability of weapons, and judged that the slight inconvenience of having to acquire weaponry after transport was a smaller problem than walking around with a futuristic weapon and a gaping hole in the stomach.
And really, how much deader would Sarah Conner have been if she'd been hit by a plasma rifle than shot in the face by a 9mm?