Which one is better to choose: SVNIT (computers) or NITK (ME)? My physics is quite weak so will it affect taking mechanical as a branch?

I would suggest you take CSE in SVNIT. In terms of placements also, CSE is better than mechanical in any college.

It only depends on your interest. If your interest is in coding, then try for computer. Try to take admission in an NIT better than SVNIT, otherwise, it is also good.

Yes, it will affect if your Physics is weak. Go for SVNIT CSE if you have interest in coding & designing. Mechanical engineering needs a high level of interest in Physics.