One of the best things about a nice quiet, well-behaved dog like Tilly, is that she tends to take everything in stride. Very little, if anything, can seem to get her too excited. Sure, she loves to play, but beyond this, she doesn't go nuts when the doorbell rings, or freak out when you have to leave her at home during the day. About the only thing that seems to put a bit of a kink in her mellow state of mind, is grooming.
The good news is that with a little hard work on both your parts, you can make the whole process easier for both of you. Think of this time as your personal bonding time with Tilly and be sure to use lots of praise and plenty of treats in the beginning.
Most quiet dogs tend to be relatively docile by nature. This should make grooming easy, but Tilly may still get nervous around the brushes, shears, combs, clippers, and so forth used for weekly and monthly grooming. Take your time introducing Tilly to each of the different tools, let her set the pace, and make it fun.
Even the quietest and most docile of dogs can be skittish when it comes to being groomed. Take your time, let your pup get used to the tools you plan to use and make the process fun. Use plenty of treats and use this time to truly bond with your pup. Keep sessions short, full of fun treat breaks and before long, your pup will look forward to this weekly grooming sessions.