Writing a letter of recommendation as a graduate student
[H]ow much does the position of the person writing a recommendation letter matter, as opposed to his/her academic familiarity with the student? 


It matters very highly.  For most graduate programs it would be better to have a letter from a very eminent and trusted person which simply says "Student X's performance in my class convinces me that she will be successful in a top master's/PhD program.  I highly recommend that you admit her." than a more personally insightful letter from a less well known faculty member, let alone someone who has not even completed the degree that the student is applying for.  If you have not yourself completed a master's degree, how can you certify that the student will be able to do so successfully?  (Well, of course it may well be that you probably can, but what degree of trust can the reader put into your letter?  Not very much.)

In general, I would recommend that even postdocs and temporary faculty should defer to more senior faculty, if possible, when writing letters, and in any case the student should make sure to get at least one letter from a senior person. If someone who has a PhD (let's say) but is otherwise very junior can say something about the student that other faculty cannot, it could be a good idea to send along a letter, but it would be better to have that be an additional letter beyond the number required.  However, for someone like you who has not even completed the degree the student is applying for, I would simply say that you should not write a letter for the student.  If you want to help, I would recommend that you find a faculty member who is senior enough but doesn't know the student very well and give them the information that you wanted to convey in your own letter.  (Don't write the letter for them!  Just give them the information.)  It helps of course to find a faculty member that you are comfortable with.

By the way, if you are in the habit of mentoring grad-school bound undergraduates, you 
would be doing them a favor if you let them know as early as possible that it is in their best interest to make significant contacts with senior faculty as well as with you.