Excellent question, and one which I believe could be answered with a number of different plays that would make sense. For me, I believe the way one should play these hands depends on what kind of game you are in, what kind of chip stack you and everyone else has, as well as the "look" of your recent play...
It never makes sense to me to simply call the blind with these cards, but I do think it often makes sense to restrain the bet to a soft raise when in the position you were in. 2.5 times the BB seems perfect to me, because you don't want a terrible hand sitting on BB to be able to limp in and then luck into something big on the flop. The soft raise also empowers you to "see" your opponents with more clarity, because the soft raise is still inviting to middling hands. From there, I would continue to bet soft so long as a flush or straight draw isn't on the board. If one of those two draws are on the board, then I would over bet hard as shit on both the flop and turn - unless they made their hand, then I would just check, and only call small raises - so you put pressure on your opponent to fold. That style of play is the most profitable way to play those hands, other than going all in pre-flop. Think of it this way, getting dealt pairs statistically gets weaker over the life of a hand, which means you need to play with a style that defends against draws to maximize one's profitability.
Just my own questionable opinion
Best of luck moving forward friend!