I completed and passed Weil's Video Interview in the summer for their TC and got through to first-round interview.
I'm afraid I can't exactly remember the questions I was asked, however, I believe the questions were along the lines of:
i) why commercial law?
ii) why Weil? (mentioning a recent deal that attracted you to the firm & dropping names of clients works well here)
iii) what does private equity (PE) means to you and why it is of interest to you?
iv) how does Weil stands out from their competitors? (worth identifying one or two competitors mainly in the PE space), and
v) a time you've demonstrated one of their competencies. (which you can find online)
I hope this helps and good luck!