Inner tube size and can you feel the slime in inner tubes?
I see this as a two part question. 


A 1.5- 2.125 width tube will fit in a 2.4" tyre fine. 


I carry 2" wide tubes in my seat pack when I go cycling as a spare tube for my 2.35 tyres. I do so purely as it fits nicer in my pack and my tyres are tubeless. So if I get a puncture, I put the tube in and fix the tubeless when I get home. 


You won't notice the weight but Slime might not work as well with over streched inner tubes. 


When you fit a slimmer inner tube in a wider tyre, it streches more. So if you get a puncture with a slimmer inner tube, the slime has to work harder (than with a correct size tube) to plug the hole as it is more likely to burst bigger due to the over streching. 

Personally I would rather invest in a more puncture proof tyre than in using Slime.