How to gain weight in a healthy way?

I know this has been asked on here before (albeit a long time ago) but I just want some new answers. I’m also looking for more than “eat more” because I eat plenty. I weigh about 125 and I’m 5’9”. I used to be 140 when I was a freshman in college, which was about 5 years ago. I lost weight unintentionally and never gained it back. What makes it worse is that whenever I’m sick (like now) I tend to lose MORE weight which puts me in unhealthy weight territory. I run 3 miles 3 times a week for exercise. I don’t lift, though I probably should. Is there a way for me to gain healthy weight? Oh and I can’t do any type of regimen with heavy dairy because I’m allergic to milk. If I eat cheese, it has to be in very small portions or I will get sick.