Answering from the point of view of a physical scientist, and in keeping with my personal take on what kinds of help are appropriate or inappropriate.
(I haven't been a TA for a long time, but I teach at an all-undergrad department so I have to be my own TA.)
These are great teachable moments if you have the time (and it can take a lot of time).
You don't check their homework, you ask them to explain their solutions to you.
But there is a catch: you don't let them get away with "I used this formula, and I solved for [variable]"; instead, make them explain their logic and the conceptual basis of their work step by step. When they are stuck or are proceeding incorrectly, you probe their understanding of the problem in a Socratic style.
The kind of questions you might ask include:
Most students will find those questions very difficult at first, but as they become more adept at handling the questions they should see their homework and exam scores improve markedly.
If they have the patience they will solve the problem for themselves right there in your office.
Though this is very time consuming most students will not be regulars. Some will simply become frustrated at what they see as your unwillingness to "help" and look elsewhere; and others will get better at the discipline: as the term progresses they'll bring you fewer problems and ask more perceptive questions about them.
In addition to wanting to talk about formulas first, they are going to want to talk about values ("and then I plugged in the 18 from the problem..."). Don't let them do that either. Make they say what quantity it was ("and then inserted the given initial velocity ...").
Beginners are all about numbers and formulas, but learning the discipline is about principles first, problem solving process second, and particular results last.
Philosophical note: As I see it the purpose of homework is to facilitate learning. I wouldn't even grade it except that there is no other way to insure that they will do it. That's why it doesn't bother me that they are getting a lot of support doing the homework for my class: when they come to me I get to make it a learning experience for them.
(The first time they come in they may think they are going to get one for free, but they're in for some skull sweat.)
Admittedly, I get to decide that for my own class and when you are a TA, you may have to abide by the professor's opinion about how much and how directly you should help with assignments.