So there is this guy at my gym and I'm pretty sure he has interest because I noticed that he looks at me a lot, does it often, usually is near/around me, his friend/s look at me often too but only when "he" is there. Plus he once did treadmill running next to me (I was doing shoulders and he was next to me but between glass, we prob at least a meter away.. strange) and he did talk to me first by asking "hey are you using this machine while I was already using something and he only did 3 reps/counts and left... strange

The 1st convo went like this M: me D: gym guy
M: - hey, how's it going?
CA: - Oh hey, going good. You?
M:- Sorry, its kinda loud
CA: - Oh going good. You?
M: - Oh good too, anyway I see you around often and I just wanted to say hi "leave"
despite it was short it felt nice since he smiled a lot and gave me good eye contact.
The second time I talked to him was to ask his name during the short convo he didn't smile but gave eye contact the whole time plus when I half smiled..(i dont know what to called it I guess chilled smile?) he just gave me a nod "not the one you do when you check out a chick or giving a hi signal to your friend, he did just up down nod".
So this thing is been going on for months now and he hasn't really done anything excluding the stuff I listed but I feel like I'm not doing my part since I don't look or smile at him (well I look but just bad timing haha)

I usually go to gym with my bro and I made it clear that my gym buddy is my bro but on Thursday I'm going to gym with a friend (girl) if that helps (btw Thursday is tomorrow for me so some opinions would be good :D)

A few people told me to give up on this guy but should I? :/
What do you think I should? Smile at him more and often? say something? uhhh help
by the way I go to gym for working out and I know about unwritten rules and how some don't like that stuff at gym and I agree but I don't mind small talk