No, there's no negative effect on the transpoert mechanism. The SID only weighs 2.8 gramm that's about 0.089 oz.
I have no experience with the SID but have used a similar product from Holland called the CD MAT by Van Art in conjunction with an Audio Aero Capitole MKII SE top loading cd player. The improvements noted with the SID are consistent with the CD MAT as well (improved dynamics, better separation, blacker backgrounds, cleaner mids and highs, etc) BUT I personally felt that the PACE of the music was slightly slowed down. For jazz recordings this effect was actually quite beneficial in my opinion (Miles Davis, John Coltrane, Nina Simone) but for classical music it was definitely not ... especially where allegro pieces were involved as it killed the rhythm of the piece. I always wandered if this was due to the weight of the CD MAT affecting the spindle speed slightly but I can't say for sure.
In any case, for the differences to be clear, the system needs to be up to par, cd needs to be demagnitized ahead of the process and if a test & burn-in cd is available that should also be played on the system for a few hours/days ahead. That way, the improvement will be more noticeable as opposed to just popping one of these mats in and expecting to be blown away.
Tried almost all mats available (still have a SID in a jewel case matter of fact)
The one that works best for me is the De Mat by Van Art Speak, a carbon impregnated rubber mat with a small lip that fits over the CD (not recommended for tray load mechanisms however)
I also attached a Herbies Grungebuster Mat underneath the puck of my CEC top loader for additional damping, a very highly effective combination here.